Operations with Rational Functions
Instructions
- The introductory video below explains 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.
When you are done, you can use the graph to pick another section or use the buttons to go to the next section
Learning Objectives
- 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
Concept Video(s)
Exercises
1.
- \(\dfrac{1}{2x},\quad\) \(x\neq 0\)
- Not reducible
- \(\dfrac{3}{x},\quad\) \(x\neq 0,-3\)
- Not reducible
2.
- \(\dfrac{3+y}{x},\quad\) \(x\neq 0\)
- \(\dfrac{6-x}{x-2},\quad\) \(x\neq 2\)
- \(\dfrac{x^2+x+14}{x(x+7)},\quad\) \(x\neq 0,\) \(x\neq -7\)
3.
- \(\dfrac{28}{45} x,\quad\) \(x\neq 0\)
- \(\dfrac{2(x+1)^2}{x},\quad\) \(x\neq 0, x\neq 1\)
- \(\dfrac{2}{x+3}+\dfrac{1}{h},\quad \) \(x\neq -3, h\neq 0\)
4.
\(\dfrac{7x+3}{6x+6}, \quad\) \(x\neq -1\)
5.
\(\dfrac{x^3+2x^2-4x+5}{x-1}=x^2+3x-1+\dfrac{4}{x-1}\)