Copyright © 2008 Pearson Education, Inc Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Multiplying and Dividing Rational Expressions 7.2 Multiplying and Dividing Rational Expressions Multiply rational expressions. Divide rational expressions. 1 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Multiply rational expressions. Objective 1 Multiply rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 3

Multiply rational expressions. The product of two fractions is found by multiplying the numerators and multiplying the denominators. Rational expressions are multiplied in the same way. The product of the rational expressions and is That is, to multiply rational expressions, multiply the numerators and multiply the denominators. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 4

EXAMPLE 1 Multiply. Write each answer in lowest terms. Solution: Multiplying Rational Expressions Multiply. Write each answer in lowest terms. Solution: It is also possible to divide out common factors in the numerator and denominator before multiplying the rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 5

EXAMPLE 2 Multiply. Write the answer in lowest terms. Solution: Multiplying Rational Expressions Multiply. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 6

EXAMPLE 3 Solution: Multiply. Write the answer in lowest terms. Deciding whether Ordered Pairs Are Solutions of an Equation Multiply. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 7

Divide rational expressions. Objective 2 Divide rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 8

Divide rational expressions. Division of rational expressions is defined as follows. If and are any two rational expressions with then That is, to divide one rational expression by another rational expression, multiply the first rational expression by the reciprocal of the second rational expression. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 9

EXAMPLE 4 Divide. Write each answer in lowest terms. Solution: Dividing Rational Expressions EXAMPLE 4 Divide. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 10

EXAMPLE 5 Divide. Write the answer in lowest terms. Solution: Dividing Rational Expressions EXAMPLE 5 Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 11

EXAMPLE 6 Divide. Write the answer in lowest terms. Solution: Dividing Rational Expressions EXAMPLE 6 Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 12

EXAMPLE 7 Divide. Write in the answer in lowest terms. Solution: Dividing Rational Expressions (Factors Are Opposites) Divide. Write in the answer in lowest terms. Solution: Remember to write −1 when dividing out factors that are opposite of each other. It may be written in the numerator or denominator, but not both. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 13

Multiplying or Dividing Rational Expressions. In summary, use the following steps to multiply or divide rational expressions. Step 1: Note the operation. If the operation is division, use the definition of division to rewrite it as multiplication. Step 2: Multiply numerators and denominators. Step 3: Factor all numerators and denominators completely. Step 4: Write in lowest terms using the fundamental property. Steps 2 and 3 may be interchanged based on personal preference. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 14