Chapter 8: Rational and Radical Functions

Section 2: Multiplying and Dividing Rational Expressions

Objectives

Simplify rational expressions. Multiply and divide rational

expressions.

Vocabulary

rational expression

Why Learn This?

You can simplify rational expressions to determine the probability of hitting an archery target.

(See Exercise 35.)

8.2: Multiplying and Dividing Rational Expressions

In Lesson 8-1, you worked with inverse variation functions such as y = 5/x.

The expression on the right side of this equation is a rational expression.

A rational expression is a quotient of two polynomials.

Other examples of rational expressions include the following:

8.2: Multiplying and Dividing Rational Expressions

Because rational expressions are ratios of polynomials, you can simplify them the same way as you simplify fractions.

Recall that to write a fraction in simplest form, you can divide out common factors in the numerator and denominator.

Example 1: Simplifying Rational Expressions

Example 2: Simplifying by Factoring -1

8.2: Multiplying and Dividing Rational Expressions

You can multiply rational expressions the same way that you multiply fractions.

Example 3: Multiplying Rational Expressions

8.2: Multiplying and Dividing Rational Expressions

You can also divide rational expressions.

Recall that to divide by a fraction, you multiply by its reciprocal.

Example 4: Dividing Rational Expressions

Example 5: Solving Simple Rational Equations

OTL

Page 580-581 1-35