Simplifying Rational Expressions ALGEBRA 1 LESSON 12-3 pages 654–656  Exercises 1. 2. 3. 4. 5. 3x 6. 7. 8. 9. 2a + 3 4 1 7x 3 2 x + 2 x2 b + 4 m – 7 10. 11. 12. 13. 14. b + 3 15. 16. –1 17. 18. –2 19. – w w – 7 a + 1 5 m + 3 m + 2 c – 4 c + 3 m – 2 –4 t + 1 20. – 21. – 22. 36 min 23. 13 min 24. 13 min 25. 26. 27. 28. 29. w – 4 2r – 1 r + 5 v + 5 7z + 2 z – 1 4a2 2a – 1 5t – 4 3t – 1 3(z + 4) z3 12-3

Simplifying Rational Expressions ALGEBRA 1 LESSON 12-3 30. 31. – 32. 33. 34. Answers may vary. Sample: 35. a. i.  ii.  b. ; 36. The student canceled terms instead of factors. 37. –3 is not in the domain of . 38. 39. 40. 41. 42. 43. 44. 45. sometimes 46. sometimes 47. never 48. C 49. I 50. B 51. D 52. C 53. [2] The student put the 4 in the numerator rather than in the denominator. = [1] no explanation OR incorrectly simplified expression 2s + 1 s2 5w 5w + 6 2a + 1 a + 3 1 4 3y 4(y + 4) 4 + 3m m – 7 –c(3c + 5) 5c + 4 t + 3 3(t + 2) m – n m + 10n 3 (x – 2)(x + 3) a – 3b a + 4b 2b + 4h bh 2h + 2r rh 6v – 7w 3v – 2w x – 5 4x – 20 4 9 4 9 x – 5 4(x – 5) 1 4 x2 – 9 x + 3 12-3

Simplifying Rational Expressions ALGEBRA 1 LESSON 12-3 54. vertical asymptote: x = 0; horizontal asymptote: y = 2; 55. vertical asymptote: x = 4; horizontal asymptote: y = 0; 56. vertical asymptote: x = 0; horizontal asymptote: y = –4; 57. 10 2 58. a2b3c4 b 59. 2 2 60. 61. y = x2, y = –2x2, y = 3x2 62. y = x2, y = x2, y = x2 63. y = 0.5x2, y = 2x2, y = –4x2 64. y = –x2, y = 2.3x2, y = –3.8x2 2 5m2 1 4 3 5 12-3