Chap7 Section6

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 7.6 Complex Fractions 703 Version: Fall 2007 7.6 Exercises In Exercises 1 - 6 , evaluate the function at the given rational number. Then use the first or second technique for simpli- fying complex fractions explained in the narrative to simplify your answer. 1. Given f ( x ) = x + 1 2 x , evaluate and simplify f (1 / 2) . 2. Given f ( x ) = 2 x x + 5 , evaluate and simplify f (3 / 2) . 3. Given f ( x ) = 2 x + 3 4 x , evaluate and simplify f (1 / 3) . 4. Given f ( x ) = 3 2 x x + 5 , evaluate and simplify f (2 / 5) . 5. Given f ( x ) = 5 2 x x + 4 , evaluate and simplify f (3 / 5) . 6. Given f ( x ) = 2 x 9 11 x , evaluate and simplify f (4 / 3) . Copyrighted material. See: 1 In Exercises 7 - 46 , simplify the given complex rational expression. State all re- strictions. 7. 5 + 6 x 25 x 36 x 3 8. 7 + 9 x 49 x 81 x 3 9. 7 x 2 5 x 7 8 x 7 + 3 x + 8 10. 9 x + 4 7 x 9 9 x 9 + 5 x 4 11. 3 + 7 x 9 x 2 49 x 4
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704 Chapter 7 Rational Functions Version: Fall 2007 12. 2 5 x 4 x 2 25 x 4 13. 9 x + 4 + 7 x + 9 9 x + 9 + 2 x 8 14. 4 x 6 + 9 x 9 9 x 6 + 8 x 9 15. 5 x 7 4 x 4 10 x 4 5 x + 2 16. 3 x + 6 + 7 x + 9 9 x + 6 4 x + 9 17. 6 x 3 + 5 x 8 9 x 3 + 7 x 8 18. 7 x 7 4 x 2 7 x 7 6 x 2 19. 4 x 2 + 7 x 7 5 x 2 + 2 x 7 20. 9 x + 2 7 x + 5 4 x + 2 + 3 x + 5 21. 5 + 4 x 25 x 16 x 3 22. 6 x + 5 + 5 x + 4 8 x + 5 3 x + 4 23. 9 x 5 + 8 x + 4 5 x 5 4 x + 4 24. 4 x 6 + 4 x 9 6 x 6 + 6 x 9 25. 6 x + 8 + 5 x 2 5 x 2 2 x + 2
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Section 7.6 Complex Fractions 705 Version: Fall 2007 26. 7 x + 9 + 9 x 2 4 x 2 + 7 x + 1 27. 7 x + 7 5 x + 4 8 x + 7 3 x + 4 28. 25 16 x 2 5 + 4 x 29. 64 x 25 x 3 8 5 x 30. 4 x + 2 + 5 x 6 7 x 6 5 x + 7 31. 2 x 6 4 x + 9 3 x 6 6 x + 9 32. 3 x + 6 4 x + 4 6 x + 6 8 x + 4 33. 9 x 2 64 x 4 3 8 x 34. 9 x 2 25 x 4 3 5 x 35. 4 x 4 8 x 7 4 x 7 + 2 x + 2 36. 2 7 x 4 49 x 2 37. 3 x 2 + 8 x 9 + 3 x 2 81 9 x 2 81 + 9 x 2 8 x 9 38. 7 x 2 5 x 14 + 2 x 2 7 x 18 5 x 2 7 x 18 + 8 x 2 6 x 27 39. 2 x 2 + 8 x + 7 + 5 x 2 + 13 x + 42 7 x 2 + 13 x + 42 + 6 x 2 + 3 x 18
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706 Chapter 7 Rational Functions Version: Fall 2007 40. 3 x 2 + 5 x 14 + 3 x 2 7 x 98 3 x 2 7 x 98 + 3 x 2 15 x + 14 41. 6 x 2 + 11 x + 24 6 x 2 + 13 x + 40 9 x 2 + 13 x + 40 9 x 2 3 x 40 42. 7 x 2 + 13 x + 30 + 7 x 2 + 19 x + 90 9 x 2 + 19 x + 90 + 9 x 2 + 7 x 18 43. 7 x 2 6 x + 5 + 7 x 2 + 2 x 35 8 x 2 + 2 x 35 + 8 x 2 + 8 x + 7 44. 2 x 2 4 x 12 2 x 2 x 30 2 x 2 x 30 2 x 2 4 x 45 45. 4 x 2 + 6 x 7 4 x 2 + 2 x 3 4 x 2 + 2 x 3 4 x 2 + 5 x + 6 46. 9 x 2 + 3 x 4 + 8 x 2 7 x + 6 4 x 2 7 x + 6 + 9 x 2 10 x + 24 47. Given f ( x ) = 2 /x , simplify f ( x ) f (3) x 3 . State all restrictions. 48. Given f ( x ) = 5 /x , simplify f ( x ) f (2) x 2 . State all restrictions. 49. Given f ( x ) = 3 /x 2 , simplify f ( x ) f (1) x 1 .
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