R.5 day2 Multiply and Divide Rational Expressions Learning Target: You will be able to multiply and divide rational expressions, and simplify the product or quotient.

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 - 3

EXAMPLE 1 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 - 4

Multiply the fractions Reduce before multiply.

Multiply the fractions Reduce before multiply.

Example 2 Multiply rational expressions Step 1: Factor and Multiply

Checkpoint Multiply the expression 6x² + 18x x² - x – 2 x² + x – 6 * x² - 7x – 8 6x(x + 3)(x-2)(x+1) (x+3)(x-2)(x-8)(x+1) 6x x-8

More Examples Multiply the expressions. Simplify the result.

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 - 12

EXAMPLE 4 Solution: Dividing Rational Expressions Divide. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 13

EXAMPLE 5 Solution: Dividing Rational Expressions Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 14

EXAMPLE 6 Solution: Dividing Rational Expressions Divide. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7.2 - 15

EXAMPLE 7 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 - 16

Divide the Rational Expressions You can only Reduce when Multiplying

Example 4 Divide rational expressions Step 1: Multiply by reciprocal   Step 2: Factor and Multiply   Step 3: Simplify

More Examples Divide each expression. Simplify the result.

Homework R.5 (pg 53) #33-49 odd