A42 APPENDIX Review Simplifying a Complex Rational Expression Simplify: − + − − ≠ x x x x x 4 2 2 2 1 0, 2, 4 2 Solution EXAMPLE 9 We use Option 1. ( ) ( )( ) ( )( ) ( ) − + − − = − + − − − − = + − − − − = + − − − = + − − ⋅ − = + − x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 4 2 2 2 1 4 2 4 4 2 2 2 8 4 2 2 4 2 4 2 4 2 4 2 4 4 2 2 2 Now Work problem 33 Skill Building In Problems 7–14, reduce each rational expression to lowest terms. 7. + − x x 3 9 9 2 8. + + x x x 4 8 12 24 2 9. − − x x x 2 3 6 2 10. + x x x 15 24 3 2 2 11. − x x x 24 12 6 2 2 12. + + − x x x 4 4 4 2 2 13. − − − y y y 25 2 8 10 2 2 14. − − + + y y y y 3 2 3 5 2 2 2 In Problems 15–36, perform the indicated operation and simplify the result. Leave your answer in factored form. 15. + ⋅ − x x x x 3 6 5 4 2 2 16. ⋅ + x x x 3 2 6 10 2 17. − ⋅ − x x x x 4 16 64 2 2 2 3 18. + ⋅ + − x x x x 12 1 4 2 2 3 19. − + x x x x 8 1 10 1 2 20. − − + x x x x x 2 4 4 4 12 2 21. − + − x x x x 4 4 4 16 2 22. + − − x x x x 3 3 9 9 2 3 23. − − − x x x 2 3 4 2 3 2 24. − − − x x x 3 2 1 9 2 1 2 25. − + x x x 4 1 2 26. − + + x x x x 1 1 3 2 A.5 Assess Your Understanding Concepts and Vocabulary 1. When the numerator and denominator of a rational expression contain no common factors (except 1 and −1 ), the rational expression is in . 2. LCM is an abbreviation for . 3. True or False The rational expression − − x x x 2 4 2 3 is reduced to lowest terms. 4. True or False The LCM of + x x 2 6 3 2 and + x x 6 4 4 3 is ( ) + x x 4 1 . 3 5. Multiple Choice Choose the statement that is not true. Assume ≠ ≠ b c 0, 0 , and ≠ d 0 as necessary. (a) = ac bc a b (b) + = + a b c b a c b (c) − = − a b c d ad bc bd (d) = a b c d ac bd 6. Multiple Choice Choose the rational expression that simplifies to −1 . (a) − − a b b a (b) − − a b a b (c) + − a b a b (d) − + b a b a 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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