926 CHAPTER 9 Systems and Matrices 6. In Exercise 5, after clearing fractions to decompose, the equation 3x - 1 = A12x2 + 122 + 1Bx + C21x212x2 + 12 + 1Dx + E21x2 results. If we let x = 0, what is the value of A? Find the partial fraction decomposition for each rational expression. See Examples 1–4. 7. 5 3x12x + 12 8. 3x - 1 x1x + 12 9. 4x + 2 1x + 2212x - 12 10. x + 2 1x + 121x - 12 11. x x2 + 4x - 5 12. 5x - 3 x2 - 2x - 3 13. 4 x11 - x2 14. 9 x1x - 32 15. 4x2 - x - 15 x1x + 121x - 12 16. 3 1x + 121x + 32 17. 2x + 1 1x + 223 18. 2x 1x + 121x + 222 19. x2 x2 + 2x + 1 20. 2 x21x + 32 21. x3 + 4 9x3 - 4x 22. x3 + 2 x3 - 3x2 + 2x 23. -3 x21x2 + 52 24. 1 x21x2 - 22 25. 3x - 2 1x + 4213x2 + 12 26. 2x + 1 1x + 121x2 + 22 27. 1 x12x + 1213x2 + 42 28. 3 x1x + 121x2 + 12 29. 2x5 + 3x4 - 3x3 - 2x2 + x 2x2 + 5x + 2 30. 6x5 + 7x4 - x2 + 2x 3x2 + 2x - 1 31. 3x - 1 x12x2 + 122 32. x4 + 1 x1x2 + 122 33. -x4 - 8x2 + 3x - 10 1x + 221x2 + 422 34. 3x4 + x3 + 5x2 - x + 4 1x - 121x2 + 122 35. 5x5 + 10x4 - 15x3 + 4x2 + 13x - 9 x3 + 2x2 - 3x 36. 3x6 + 3x4 + 3x x4 + x2 37. x2 x4 - 1 38. -2x2 - 24 x4 - 16 39. 4x2 - 3x - 4 x3 + x2 - 2x 40. 2x + 4 x3 - 2x2
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