Operations with Rational Functions
Instructions
- The first videos below explain the concepts in this section.
- This page also includes exercises that you should attempt to solve yourself. You can check your answers and watch the videos explaining how to solve the exercises.
Concepts
- Operations between fractions including addition, subtraction, multiplication, and division
- How to simplify rational expressions
- How to add and subtract rational expressions by finding a common denominator
- How to multiply and divide rational expressions
- How to do polynomial long division
Exercises
Directions: You should attempt to solve the problems first and then watch the video to see the solution.
- Reduce the following rational expressions, if possible.
- \(\dfrac{2}{4x}\)
- \(\dfrac{6}{4+x}\)
- \(\dfrac{3x+9}{x^2+3x}\)
- \(\dfrac{x+1}{x^2+x+1}\)
- Perform the following operations:
- \(\dfrac{3}{x}+\dfrac{y}{x}\)
- \(\dfrac{7}{x-2}-\dfrac{x+1}{x-2}\)
- \(\dfrac{2}{x}+\dfrac{x-1}{x+7},\quad\) \(x\neq 0, x\neq -7\)
- Perform the following operations
- \(\dfrac{2}{3}\cdot \dfrac{4}{5}\div \dfrac{6}{7x},\quad\) \(x\neq 0\)
- \(\dfrac{2x^2-2}{x}\cdot \dfrac{x+1}{x-1},\quad\) \(x\neq 0, x\neq 1\)
- \(\dfrac{ \frac{2h}{x+3} +1}{h},\quad\) \(x\neq -3, h\neq 0\)
- Perform the following operations and simplify if possible \[\dfrac{x}{x+1}\cdot \dfrac{2}{3}+\dfrac{3}{8}\div \dfrac{3}{4}\]
- Do polynomial long division to simplify the following rational function: \[\frac{x^3+2x^2-4x+5}{x-1},\quad x\neq 1\]
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