1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Multiply and divide rational expressions. Simplify rational expressions, including complex fractions. 8.3 Multiplying and Dividing Rational Expressions

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Term complex fraction 8.3 Multiplying and Dividing Rational Expressions

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Multiply, divide, and simplify rational expressions, including complex fractions. 8.3 Multiplying and Dividing Rational Expressions x 2 + 5x + 4 x 2 + 4x + 3 x 2 + 3x – 4 x 2 + 3x  x 2 + 5x + 4 x 2 + 4x + 3 x 2 + 3x x 2 + 3x – 4  (x + 1)(x + 4) (x + 3)(x + 1)  x(x + 3) (x + 4)(x – 1) Multiply by the reciprocal. Factor each polynomial. Simplify. x x – 1 =

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Multiply, divide, and simplify rational expressions, including complex fractions. 8.3 Multiplying and Dividing Rational Expressions x 2 – 2x – 3 x 2 – 9 x 2 + 8x + 7 x 2 + x – 6 x 2 – 2x – 3 x 2 – 9 x 2 + 8x + 7 x 2 + x – 6  Rewrite horizontally.

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Multiply, divide, and simplify rational expressions, including complex fractions. 8.3 Multiplying and Dividing Rational Expressions x 2 – 2x – 3 x 2 – 9 x 2 + 8x + 7 x 2 + x – 6  x 2 – 2x – 3 x 2 – 9 x 2 + x – 6 x 2 + 8x + 7  (x – 3)(x + 1) (x + 3)(x – 3)  (x – 2)(x + 3) (x + 1)(x + 7) Multiply by the reciprocal. Factor each polynomial. Simplify. (x – 2) (x + 7) = TOC