# Chapter 9: Rational Functions

Difficulty Level:

**At Grade**Created by: CK-12

## Introduction

This chapter deals with functions that have the variable in the denominator of a fraction. First, we will discuss the concept of variation and how that relates to a rational function. Next, we will graph several different types of rational functions followed by multiplying, dividing, adding, and subtracting rational expressions. Lastly, we will solve rational equations.

Chapter Outline

- 9.1.
## Direct Variation

- 9.2.
## Inverse Variation

- 9.3.
## Joint Variation

- 9.4.
## Graphing Rational Functions in Standard Form

- 9.5.
## Graphing when the Degrees of the Numerator and Denominator are the Same

- 9.6.
## Graphing when the Degrees of the Numerator and Denominator are Different

- 9.7.
## Simplifying Rational Expressions

- 9.8.
## Multiplying Rational Expressions

- 9.9.
## Dividing Rational Expressions

- 9.10.
## Adding and Subtracting Rational Expressions with Like Denominators

- 9.11.
## Adding and Subtracting Rational Expressions where One Denominator is the LCD

- 9.12.
## Adding and Subtracting Rational Expressions with Unlike Denominators

- 9.13.
## Complex Fractions

- 9.14.
## Solving Rational Equations using Cross-Multiplication

- 9.15.
## Solving Rational Equations using the LCD

### Chapter Summary

## Summary

This chapter covers variation, graphing rational functions, simplifying, multiplying, dividing, adding and subtracting rational expressions, and solving rational equations.

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Description

This chapter covers graphing and solving rational functions and equations.

Difficulty Level:

At Grade
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Subjects:

Date Created:

Jan 08, 2016
Last Modified:

Jun 09, 2016
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