1 4 homework
- 1. Multiplication and Division of Rational Expressions Ex A. Simplify. Do not expand the results. 3 3.12x6 * 5 14 3 1. 10x * 2 3 2. 5x3 * 10x 4. 5x3 * 10x 5x 6x 5. 15x * 16 4 6. 10 * 183 7. 56x6* 635 8. 75x * 42 3 4 25x 9x4 5x 27 8x 49 25x 2x – 4 * 5x + 10 6 – 4x x – 2 9. 2x + 4 3x – 6 10. 3x – 2 * 2x + 4 9x – 12* 2 – x 4–x * x+4 11. 2x – 4 8 – 6x 12. –x – 4 x – 4 3x – 9 * 3 – x 42 – 6x 4 – 2x 13. 15x – 5 5 – 15x 14. –2x + 14 * –7x + 14 (x2 + x – 2 ) (x2 – 4 ) (x2 + 2x – 3 ) (x2 – 2x – 3) 15. 16. * (x – 2) * (x2 – x) (x – 9) 2 (x2 – x – 2 ) (x2 – x – 2 ) (x2 + x ) (x2 + 5x – 6 ) (x2 – 5x + 6) 17. 18. 2 * (x – 1) 2 * (x2 + 2x + 1) (x + 5x + 6) (x2 – 5x – 6 ) (x2 – 3x – 4 ) (x2 – 3x + 2) 20. (– x + 6 – x ) (6 – x – x) 2 2 19. * * (x + 5x + 6) (x2 – x – 12 ) 2 (x2 – 1) (x2 – 2x – 8)
- 2. Multiplication and Division of Rational Expressions Ex. A. Simplify. Do not expand the results. (2x2 + x – 1 ) ÷ (4x2 – 1) (3x2 – 2x – 1) (x2 + x – 2 ) 21. 22. (1 – 2x) (2x – x ) 2 (1 – 9x2) ÷ (x2 + 4x + 4) (x2 – x + 2) ÷ (3x2 + 4x + 1) 24. (x + 1 – 6x ) ÷ (2x + x – 1 ) 2 2 23. (3x2 – x – 2) (–x – 3x2) (–x2 – 4) (x2 – 5x – 6) (x3 – 4x) (x2 + 2) (–x3 + 9x ) (x2 + 6x + 9) 25. ÷ 26. (–x + 4x – 4) (–x + 2) 2 (x2 + 3x) ÷ (–3x2 – 9x) Ex. B. Multiply, expand and simplify the results. 27. x + 3 (x2 – 1) 28. x – 3 (x2 – 4) 29. 2x + 3 (x2 – 1) x+1 x–2 1–x 30. 3 – 2x (x + 2)(x +1) 31. 3 – 2x (3x + 2)(1 – 2x) x+2 2x – 1 32. ( x – 2 + x + 1 )( x – 3)(x + 3) x–3 x+3 33. ( 2x – 1 – x + 2 ) ( 2x – 3)(x + 2) x+2 2x – 3
- 3. Multiplication and Division of Rational Expressions Ex B. Multiply, expand and simplify the results. 34. ( 4 – x – x – 1 )( x – 3)(2x + 3) x – 3 2x + 3 35. ( 3 – x – 2x + 3 )(x – 3)(x + 2) x+2 x–3 36. ( 3 – 4x – 1 – 2x )( x + 3)(x + 1) x+1 x+3 37. ( 5x – 7 – 4 – 5x )(x – 3)(x + 5) x+5 x–3 38. ( x2– 2 – 2 x + 1 ) ( x – 3)(x + 3)(x + 1) x –9 x – 2x – 3 39. ( x2+ 3 – 2 2x + 1 ) ( x – 2)(x + 2)(x – 1) x –4 x +x–2 40. ( x – 1 – x2 x + 1 – 3 ) ( x – 3)(x + 2)(x + 1) x2 – x – 6 – 2x 41. ( x + 2 – x2 2x2x 1 3 ) ( x – 3)(x + 3)(x – 1) + x2 – 4x +3 + –
- 4. Multiplication and Division of Rational Expressions Ex. C. Break up the following expressions as sums and differences of fractions. x –4 x2 – 4 x2 + 4x – 6 2 43. 44. 42. x 2 2x2 2x 12x3 – 9x2 + 6x 46. x – x – x 8 x6 4 47. x – x 2 – x 8 6 4 45. 3x x Ex D. Use long division and write each rational expression in R the form of Q + D . 48. 2x++26 49. 3x––25 50. 4x– 1+3 x x x 51. 5x––34 52. 3x– x8 + 53. –4x – 5 x 2 1–x (x2 + x – 2 ) (2x2 + x – 3 ) (3x2 – 3x – 2 ) 54. 55. 56. (x – 1) (x – 2) (x + 2) (–x2 + 4x – 3 ) (4x2 + 2 ) (5x2 – 1 ) 57. 58. 59. (x – 3) (x + 3) (x – 4)