 
                                            Solving Rational Equations Video 2
Solving an equation that contains rational expressions
Problem: Solve the equation \(\quad \dfrac{7}{x}-\dfrac{3}{x-2}=2.\)
 
                                            Solving an equation that contains rational expressions
 
                                            Solving equations that contain rational expressions
 
                                            Finding the domain of a function with a denominator, square root, and logarithm
 
                                            Explaining the standard form for a quadratic equation and the possible number of solutions
 
                                            Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
 
                                            Explaining when a quadratic equation does not have a real solution
 
                                            Explaining how to solve radical equations and then solving example problems
 
                                            Solving equations with even roots and checking the solutions
 
                                            Solving equations with multiple radicals
 
                                            Performing algebraic operations with rational expressions and simplifying the answer
 
                                            Finding the domain of a piecewise function and evaluating it
 
                                            Subtracting rational expressions and simplifying
 
                                            Performing operations with rational expressions and simplifying
 
                                            Performing operations with rational expressions and simplifying
 
                                            Solving an equation using the quadratic formula
 
                                            Solving a quadratic equation using the quadratic formula
 
                                            Finding the domains of expressions
 
                                            Review of limits and derivatives of inverse trigonometric functions
 
                                            Review of limits and derivatives of inverse trigonometric functions
 
                                            Continuity of Functions and the Intermediate Value Theorem
 
                                            Explaining all four cases of partial fraction decomposition
 
                                            Review of limits and derivatives of inverse trigonometric functions
 
                                            Review of limits and derivatives of inverse trigonometric functions
 
                                            Continuity of Functions and the Intermediate Value Theorem
 
                                            Explaining all four cases of partial fraction decomposition
 
                                            Determining the domain of a three-dimensional vector function
 
                                            Finding the domain of several rational functions
 
                                            Finding the domain of a rational function
 
                                            Explaining how to find any holes and vertical asymptotes of a rational function
 
                                            Finding the domain of a rational function using factoring
 
                                            Explaining domain restrictions for denominators, even roots, and logarithms
 
                                            Finding the domain of a function with a natural logarithm and denominator
 
                                            Finding the domain of even and odd roots
 
                                            Solving quadratic equations with the difference of two squares formula
 
                                            Solving quadratic equations by factoring
 
                                            Solving a quadratic equation by factoring
 
                                            Solving a quadratic equation by factoring
 
                                            Explaining the graph and properties for the parent function of quadratics
 
                                            Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
 
                                            Solving equations with odd radicals
 
                                            Explaining the general properties of even and odd root functions
 
                                            Explaining how to solve equations with power and exponential terms
 
                                            Explaining how to solve logarithmic equations
 
                                            Solving logarithmic equations with a single logarithm term
 
                                            Solving logarithmic equations with multiple logarithm terms
 
                                            Solving logarithmic equations with multiple logarithm terms on both sides
 
                                            Discussing parent functions of rational functions and their properties
 
                                            Adding and subtracting rational expressions by finding a common denominator
 
                                            Explaining how to multiply and divide rational expressions
 
                                            Explaining all four cases of partial fraction decomposition
 
                                            Solving a rational equation and checking the solutions
 
                                            Solving an equation with logarithmic functions
 
                                            Solving an equation with logarithmic functions
 
                                            Solving an equation with logarithmic functions
 
                                            Finding the maximum revenue, maximum profit, and break even quantity for given revenue and cost functions
 
                                            Finding the piecewise-defined function for a given graph along with its domain and range
 
                                            Solving an equation with exponential functions
 
                                            Finding the domain of a function that is a fraction containing exponentials and a square root
 
                                            Dividing and subtraction rational functions and simplifying the result
 
                                            Computing and simplifying the difference quotient for a rational function
 
                                            Finding the domain, intercepts, asymptotes, and holes of a rational function
 
                                            Finding the domain, intercepts, asymptotes, and holes of a rational function
 
                                            Finding the domain, intercepts, asymptotes, and holes of a rational function
 
                                            Adding and simplifying rational functions
 
                                            Subtracting rational functions and then simplifying the result
 
                                            Finding the absolute maximum and minimum of a rational function on two closed intervals
 
                                            Dividing rational expressions and simplifying
 
                                            Solving a quadratic equation by completing the square
 
                                            Finding the domains of functions
 
                                            Determining the properties of a rational function and graphing it
 
                                            Determining the properties of a rational function and graphing it
 
                                            Solving an equation with an exponential function
 
                                            Solving an equation with exponential functions by factoring
 
                                            Solving a trigonometric equation by factoring
 
                                            Solving a trigonometric equation
 
                                            Review of limits, continuity, and the Intermediate Value Theorem
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Related rates problems, differentials, linear and quadratic approximations
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Properties and derivatives of inverse trigonometric functions
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Differentials, linear approximations and quadratic approximations
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Properties and derivatives of inverse trigonometric functions
 
                                            Derivatives of exponential and logarithmic functions and the exponential model
 
                                            Derivatives of exponential and logarithmic functions and the exponential model
 
                                            Using derivatives to find properties of graphs
 
                                            Using derivatives to find properties of graphs
 
                                            Using Reimann sums and the Fundamental Theorem of Calculus
 
                                            Using Riemann sums and the Fundamental Theorem of Calculus
 
                                            Examples of integration by substitution
 
                                            Evaluating a limit with an indeterminate difference using a common denominator
 
                                            Review of work and average value
 
                                            Reviewing u-Substitution
 
                                            Using the limit definition to find derivatives of functions and vector functions
 
                                            Review of limits, continuity, and the Intermediate Value Theorem
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Related rates problems, differentials, linear and quadratic approximations
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Properties and derivatives of inverse trigonometric functions
 
                                            Using the limit definition to find derivatives of functions and vector functions
 
                                            Using the limit definition to find derivatives of functions and vector functions
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Differentials, linear approximations, and quadratic approximations
 
                                            Review of the limit definition of a derivative and calculating the derivative
 
                                            Properties and derivatives of inverse trigonometric functions
 
                                            Derivatives of exponential and logarithmic functions and the exponential model
 
                                            Using derivatives to find properties of graphs
 
                                            Using derivatives to find properties of graphs
 
                                            Using Reimann sums and the Fundamental Theorem of Calculus
 
                                            Using Reimann sums and the Fundamental Theorem of Calculus
 
                                            Examples of integration by substitution
 
                                            Review of work and average value
 
                                            Reviewing u-Substitution
 
                                            Using integrals to solve work problems and find the average value
 
                                            Finding and sketching the domain of a function of two variables
 
                                            Finding and sketching the domain of a function of two variables
 
                                            Finding the domain of a function with a square root in the denominator
 
                                            Finding the domain of a function with a root and a logarithm in the denominator
 
                                            Finding the domain of a logarithmic function
 
                                            Finding the domain of functions with even and odd roots
 
                                            Solving a linear equation algebraically
 
                                            Discussing properties of linear functions
 
                                            Discussing the types of linear graphs including horizontal and vertical lines and their properties
 
                                            How to rewrite radical terms as power terms
 
                                            Properties of exponential growth and decay functions
 
                                            Properties of the exponential function with base e
 
                                            Solving equations with exponential terms
 
                                            Solving equations with base e exponential terms
 
                                            Explaining the basic properties of logarithmic functions
 
                                            Expanding logarithmic expressions using logarithm rules
 
                                            Condensing a logarithmic expression into a single logarithm
 
                                            Finding horizontal asymptotes for rational functions
 
                                            Explaining how to do polynomial long division
 
                                            Finding horizontal asymptotes for rational functions
 
                                            Determining the end behavior and horizontal asymptotes for rational functions
 
                                            Explaining basic algebraic operations for fractions
 
                                            How to simplify rational expressions
 
                                            Solving an equation with logarithmic functions
 
                                            Solving an equation with logarithmic functions
 
                                            Finding the properties of a quadratic function such as the vertex, axis of symmetry, intercepts, etc.
 
                                            Finding the domain, intercepts, holes, and vertical asymptotes for a rational function
 
                                            Determining the domain and range of a relation and if the relation is a function
 
                                            Determining the domain and range of a relation and if the relation is a function
 
                                            Determining the domain and range of a relation and if the relation is a function
 
                                            Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
 
                                            Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
 
                                            Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
 
                                            Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
 
                                            Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
 
                                            Identifying quadratic functions and their properties
 
                                            Graphing a piecewise function
 
                                            Finding the properties of an exponential function including domain, range, end behavior, and intercepts
 
                                            Finding the properties of an exponential function including domain, range, end behavior, and intercepts
 
                                            Finding the properties of an exponential function including domain, range, end behavior, and intercepts
 
                                            Finding the domain of a function that is a fraction containing an exponential and root
 
                                            Finding the domain of a function that is a fraction containing an exponential and root
 
                                            Solving an equation with exponential functions
 
                                            Identifying the parent function and transformations for a given graph
 
                                            Finding the domain of a function containing several logarithms
 
                                            Finding the domain of a function containing a logarithm, exponential, and fraction
 
                                            Solving an equation with exponential functions
 
                                            Solving an equation with a logarithmic function
 
                                            Solving an equation with several logarithmic functions
 
                                            Finding the domain, range, end behavior, and intercepts for a logarithmic function
 
                                            Finding the domain of a function containing a logarithm, exponential, radical, and fraction
 
                                            Solving an equation an exponential function
 
                                            Multiplying two rational functions and simplifying the result
 
                                            Dividing rational functions and simplifying the result
 
                                            Finding the difference quotient for a quadratic function
 
                                            Finding the limit of a rational function algebraically
 
                                            Finding the limit of a rational function algebraically
 
                                            Solving a limit approaching negative infinity for a rational function
 
                                            Solving the limits approaching infinity and negative infinity of a rational function
 
                                            Solving the limits approaching infinity and negative infinity of a rational function
 
                                            Finding the holes and vertical asymptotes of a rational function
 
                                            Determining where a function with a fraction, square root, and logarithm is continuous
 
                                            Determining where a piecewise function is continuous algebraically
 
                                            Finding the exact value of the instantaneous rate of change
 
                                            Using the limit definition to find the derivative of a rational function
 
                                            Using the limit definition to find the derivative of a square root function
 
                                            Finding the derivative of a rational function by simplifying and using the power rule
 
                                            Finding the derivative of a function with a square root and exponential using the Product Rule
 
                                            Finding the derivative of a rational function using the Quotient Rule
 
                                            Determining the intervals where a function is increasing and decreasing
 
                                            Finding the intervals where a function is increasing/decreasing and the local extrema
 
                                            Finding intervals of increase/decrease and the local extema for revenue from a word problem
 
                                            Using the quotient rule twice to find the second derivative of a rational function
 
                                            Finding the intervals of concavity and inflection points for a function with exponentials
 
                                            Determining the intervals of concavity and inflection points from the graph of a function
 
                                            Using the second derivative test to find local extrema for a function
 
                                            Finding the absolute maximum and absolute minimum of a rational function on two closed intervals
 
                                            Finding the selling price of trucks to maximize profit given the cost and price-demand functions
 
                                            Finding the dimensions of the box with the largest volume given the amount of material to make the box
 
                                            Finding the minimum cost of a box given the volume and cost of materials
 
                                            Explaining the Intermediate Value Theorem and the Bisection Method
 
                                            Using the Intermediate Value Theorem and Bisection Method to approximate the solution of an equation
 
                                            Using derivatives to find the velocity and acceleration functions from the position function
 
                                            Simplifying an expression with radicals
 
                                            Rationalizing the denominator of a fraction with square roots
 
                                            Rationalizing the denominator of a fraction with square roots
 
                                            Factoring a quadratic
 
                                            Factoring a polynomial
 
                                            Factoring a quadratic
 
                                            Calculating the difference quotient for a rational function
 
                                            Calculating the difference quotient for function with a square root
 
                                            Calculating the difference quotient for a rational function
 
                                            Solving a polynomial equation using factoring by grouping
 
                                            Determining if an equation represents a function
 
                                            Putting a quadratic function in standard form and determining its properties
 
                                            Putting a quadratic function in standard form and determining its properties
 
                                            Finding the x-intercepts of quadratic functions
 
                                            Putting a quadratic function in standard form and determining its properties
 
                                            Finding the end behavior of a polynomial
 
                                            Finding properties of a polynomial including zeros and end behavior
 
                                            Solving a nonlinear inequality
 
                                            Solving a nonlinear inequality
 
                                            Solving a nonlinear inequality
 
                                            Restricting the domain of a function so it is one-to-one and has an inverse
 
                                            Determining algebraically the inverse of a function
 
                                            Determining algebraically the inverse of a function
 
                                            Determining algebraically the inverse of a function
 
                                            Determining properties of an exponential function
 
                                            Determining properties of an exponential function
 
                                            Determining properties of an exponential function
 
                                            Identifying the graph of an exponential function
 
                                            Solving an equation with an exponential function
 
                                            Determining properties of an exponential function
 
                                            Determining the properties of a logarithmic function
 
                                            Determining the graph of a logarithmic function
 
                                            Determining the properties of a logarithmic function
 
                                            Determining the graph of a logarithmic function
 
                                            Solving an equation with an exponential function
 
                                            Solving an equation with an exponential function
 
                                            Modeling a population size with an exponential function
 
                                            Solving a trigonometric equation
 
                                            Solving a trigonometric equation
 
                                            Solving a trigonometric equation
 
                                            Solving a trigonometric equation
 
                                            Solving a trigonometric equation
 
                                            Using a double angle formula to solve a trigonometric equation
 
                                            Using a double angle formula to solve a trigonometric equation
 
                                            Using a double angle formula to solve a trigonometric equation
 
                                            Using double angle formulas to evaluate trigonometric functions
 
                                            Using a graph to evaluate a function
 
                                            Cartesian equations and parametric equations of curves
 
                                            Reviewing the chain rule and the derivatives and limits of trigonometric functions
 
                                            Mean Value Theorem and using derivatives to find the shape of curves
 
                                            Evaluating limits of functions
 
                                            Evaluating Limits of Functions
 
                                            Approximation and Newton's Method, and limits and derivatives of exponential functions
 
                                            Limits at infinity and asymptotes, along with physics applications
 
                                            Limits at infinity, asymptotes, and tangent lines
 
                                            Approximation and Newton's Method, and limits and derivatives of exponential functions
 
                                            Mean Value Theorem and properties of a graph
 
                                            Mean Value Theorem and properties of a graph
 
                                            Riemann sums, including approximating areas under curves.
 
                                            Finding the vertical and horizontal asymptotes for a rational function
 
                                            Finding the derivative of a function using the limit definition
 
                                            Using the Quotient Rule to differentiate a rational function
 
                                            Using a linear approximation to approximate the value of a function
 
                                            Evaluating a limit using L'Hospital's Rule
 
                                            Evaluating a limit using logarithm properties
 
                                            Finding the antiderivative of a rational function
 
                                            Evaluating a a limit from the left for a rational function
 
                                            Evaluating the limit of a rational function by factoring and cancelling
 
                                            Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
 
                                            Evaluating the limit at infinity of a rational function
 
                                            Evaluating a definite integral by first simplifying the integrand
 
                                            Review of partial fractions
 
                                            Review of partial fractions
 
                                            Review of finding the radius and interval of convergence for a power series
 
                                            Review of Taylor and Maclaurin Series and their properties
 
                                            Review of Taylor Polynomials and Taylor's Inequality
 
                                            Finding a Taylor Polynomial for a function
 
                                            Integrating a rational function using u-substitution
 
                                            Integrating a rational function using u-substitution
 
                                            Integrating a function with a square root using u-substitution
 
                                            Finding the area of a region enclosed by two curves
 
                                            Finding the area of a region bounded by curves
 
                                            Finding the volume of a solid of revolution using the washer method
 
                                            Finding the volume of a solid of revolution using cylindrical shells
 
                                            Using the comparison test to determine if an improper integral converges or diverges
 
                                            Using the comparison test to determine if an improper integral converges or diverges
 
                                            Converting parametric equations into a Cartesian equation and graphing
 
                                            Using u-substitution to integrate a rational function
 
                                            Using partial fraction decomposition to rewrite and then integrate a rational function
 
                                            Using partial fraction decomposition to rewrite and then integrate a rational function
 
                                            Using partial fraction decomposition to rewrite and then integrate a rational function
 
                                            Using partial fraction decomposition to rewrite and then integrate a rational function
 
                                            Using partial fraction decomposition to rewrite and then integrate a rational function
 
                                            Proving associative and scalar multiplication properties for vectors
 
                                            Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel
 
                                            Cartesian equations and parametric equations of curves
 
                                            Reviewing the chain rule and the derivatives and limits of trigonometric functions
 
                                            Mean Value Theorem and using derivatives to find the shape of curves
 
                                            Properties of inverse trig functions and the derivative of arctangent
 
                                            Evaluating limits of functions
 
                                            Evaluating limits of functions and using the Squeeze Theorem
 
                                            Proving a property of scalar multiplication for limits using the epsilon-delta definition and using the Squeeze Theorem for Limits.
 
                                            Proving a piecewise function and a polynomial are continuous
 
                                            Approximation and Newton's Method, and limits and derivatives of exponential functions
 
                                            Limits at infinity and asymptotes, along with physics applications
 
                                            Limits at infinity, asymptotes, and tangent lines
 
                                            Finding a formula for a higher order derivative and a formula for the second derivative of a product
 
                                            Approximation and Newton's Method, and limits and derivatives of exponential functions
 
                                            Finding a formula for a higher order derivative and a formula for the second derivative of a product
 
                                            Properties of inverse trig functions and the derivative of arctangent
 
                                            Mean Value Theorem and properties of a graph
 
                                            Mean Value Theorem and properties of a graph
 
                                            Riemann sums, including approximating areas under curves.
 
                                            The definition and properties of definite integrals
 
                                            Review of partial fractions
 
                                            Review of partial fractions
 
                                            Review of finding the radius and interval of convergence for a power series
 
                                            Review of Taylor and Maclaurin Series and their properties
 
                                            Review of Taylor Polynomials and Taylor's Inequality
 
                                            Finding a Taylor Polynomial for a function
 
                                            Finding a partial fraction decomposition and integrating using partial fractions
 
                                            Finding the limit of a three-dimensional vector function
 
                                            Finding a vector equation for the tangent line to a three-dimensional vector function
 
                                            Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
 
                                            Defining variables in Python and using the variables in equations
 
                                            Evaluating a double integral over a given region by splitting it into two double integrals
 
                                            Discussing how to write the equation of a line through two given points
 
                                            Writing a linear equation of profit from a business word problem
 
                                            Solving a linear equation algebraically and showing how this relates to the graph
 
                                            Explaining the main three forms for linear equations
 
                                            Solving a linear equation algebraically and showing how this relates to the graph
 
                                            Explaining the format and possible solutions for a system of two linear equations
 
                                            Solving a system of linear equations with two variables
 
                                            Solving a system of two linear equations with two variables using the elimination method
 
                                            Solving a system of two linear equations using a TI-84 calculator
 
                                            Solving a system of two linear equations using a TI-84 calculator
 
                                            Solving a system of two linear equations using a TI-84 calculator
 
                                            Simplifying power and exponential expressions using properties of exponents
 
                                            Simplifying power and exponential expressions using properties of exponents
 
                                            Simplifying power and exponential expressions using properties of exponents
 
                                            Simplifying an expression with both power and exponential functions using properties of exponents
 
                                            Properties of exponents applied to power and exponential expressions
 
                                            Properties of multiplying and simplifying power and exponential expressions
 
                                            Properties of exponents applied to power and exponential expressions
 
                                            Explaining the terminology and rules of logarithms
 
                                            Evaluating and then finding and sketching the domain of a function of two variables
 
                                            Finding and sketching the domain of a function of two variables
 
                                            Sketching the level curves for a function of two variables
 
                                            Sketching the level curves for a function of two variables
 
                                            Explaining the format and possible solutions for a system of two linear equations
 
                                            Explaining the Pythagorean Theorem and using it to find a missing side in a right triangle
 
                                            Finding all solutions to a trigonometric equation with sine
 
                                            Solving a trigonometric equation with secant by factoring
 
                                            Solving a trig equation with sine and cosine using aPythagorean Identity
 
                                            Finding the coordinate vector of a quadratic given a basis for the vector space
 
                                            Writing the domain of functions with radicals in interval notation
 
                                            Compute and simplify the difference quotient for a rational function
 
                                            Finding the domain of a piecewise-defined function and evaluating it for given x-values
 
                                            Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
 
                                            Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
 
                                            Stating the domain in interval notation of a function with radicals, fractions, and exponentials
 
                                            Find the domain of a function in interval notation with a fraction and logarithm
 
                                            Determining if a graph represents a function and finding the domain and range