# Chapter 8: Rational Expressions and Rational Functions

**Advanced**Created by: CK-12

## Introduction

Here you'll learn all about rational expressions. You'll start by learning how to apply your factoring skills to simplifying rational expressions. You'll then learn how operations with fractions generalize to operations with rational expressions. Finally, you will learn about rational functions. You will learn what the graphs of rational functions look like and how to find the asymptotes for rational functions.

- 8.1.
## Rational Expression Simplification

- 8.2.
## Rational Expression Multiplication and Division

- 8.3.
## Rational Expression Addition and Subtraction

- 8.4.
## Graphs of Rational Functions

### Chapter Summary

## Summary

You learned that operations with rational expressions rely on factoring and operations with fractions. To multiply rational expressions, multiply across and simplify. To divide rational expressions, change the problem to a multiplication problem by multiplying the first fraction by the reciprocal of the second fraction. To add or subtract, find the lowest common denominator in order to combine the expressions.

Rational functions can be graphed on the graphing calculator as an aid for making a sketch. You can algebraically find both the vertical and horizontal asymptotes of a rational function. To find the vertical asymptotes, consider the values of \begin{align*}x\end{align*} that cause the denominator to be equal to zero and thus the function to be undefined. One method for finding horizontal asymptotes is to solve the equation of the function for \begin{align*}x\end{align*}, and then look for the values of \begin{align*}y\end{align*} that cause the denominator to be equal to zero. In the case where the degree of the numerator is less than the degree of the denominator, the horizontal asymptote will automatically be at \begin{align*}y=0\end{align*}. Rational functions will be explored in further detail in future courses like Algebra II and PreCalculus.