Adding and Subtracting Rational Expressions ALGEBRA 1 LESSON 12-6 pages 669–671  Exercises 1. 2. 3. 4. 5. 6. 7. 8. – 9. 9 2m 7 6t – 1 n + 2 n + 3 14 c – 5 2s2 + 1 4s2 + 2 6c – 28 2c + 7 –3 2 – b 1 t 2 + 1 –2t 2t – 3 10. 1 11. 2 12. –1 13. 2x2 14. 18 15. 7z 16. 35b3c 17. 18. 19. 20. 35 + 6a 15a 12 – 2x 3x 18 + 20x2 15x8 9 + 2m 24m3 21. 22. 23. 24. 25. 26. 27. 28. 29. a. + b. c. about 0.8 h 189 – 9n 7n3 45 + 36x2 20x2 17m – 47 (m + 2)(m – 7) a2 + 9a + 12 (a + 3)(a + 5) a2 + 12a + 15 4(a + 3) c2 + 7c + 20 (c + 5)(c + 3) 4t 2 + 5t + 5 t 2(t + 1) 18a + 3 (2a + 1)(2a – 1) r 0.7r 17 7r 12-6

Adding and Subtracting Rational Expressions ALGEBRA 1 LESSON 12-6 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. –y 2 + 2y + 2 3y + 1 h 2 + h + 1 2t 2 – 7 r – 2k – 6 9 + p3 –3 – x – z xy 2z k + 3km 2m2 12c – 15a abc c 3 – a3 10x + 15 x + 2 –21t + 33 2t – 3 6x (x – 3)(x + 3)2 40. 41. The student added the terms in the denominators. 42. a. + ; b. + ; c. Yes; they both represent the time it takes to make a round trip. 43. Answers may vary. Sample: Not always; the numerator may contain a factor of the LCD. 44. Answers may vary. Sample: , ; k – 1 k – 6 2 r 1.25r 18 5r d 0.8d 9 2d 2w w + 3 3w 2 w – 3 3w3 + 11w2 – 6w (w + 3)(w – 3) 45. 46. 8 47. 48. 49. 50. 51. – 52. 53. 54. 55. D 8x 2 – 1 x – 3x – 5 x(x – 5) 32x x – 5 4x 1 2x(x – 5) d + 3 d + 4 –x3 + 6x2 + 35x – 50 (a + 12)(a – 5) x + 4 5a – 8 (a + 2)(a – 5) 12-6

Adding and Subtracting Rational Expressions ALGEBRA 1 LESSON 12-6 56. H 57. D 58. [2] a. + = total time; = = = b. = = = = The ride took 1 hours. [1] one computational error OR no work shown 10 r r + 3 10(r + 3) + 10r r(r + 3) 10r + 30 + 10r 20r + 30 10(2r + 3) 10(2(12) + 3) 12(12 + 3) 10(24 + 3) 12(15) 10(27) 180 270 3 2 59. + 2x – 1 60. 5b2 – 10b + 30 – 61. 6 62. 3 63. no solution 64. ± 6.9 65. ± 3.9 66. no solution x2 60 b + 2 1 12-6