9.3E: Exercises
- Last updated
- Aug 24, 2020
- Save as PDF
- Page ID
- 49961
( \newcommand{\kernel}{\mathrm{null}\,}\)
Practice Makes Perfect
Add and Subtract Rational Expressions with a Common Denominator
In the following exercises, add.
1. 215+715
- Answer
-
35
2. 724+1124
3. 3c4c−5+54c−5
- Answer
-
3c+54c−5
4. 7m2m+n+42m+n
5. 2r22r−1+15r−82r−1
- Answer
-
r+8
6. 3s23s−2+13s−103s−2
7. 2w2w2−16+8ww2−16
- Answer
-
2ww−4
8. 7x2x2−9+21xx2−9
In the following exercises, subtract.
9. 9a23a−7−493a−7
- Answer
-
3a+7
10. 25b25b−6−365b−6
11. 3m26m−30−21m−306m−30
- Answer
-
m−22
12. 2n24n−32−18n−164n−32
13. 6p2+3p+4p2+4p−5−5p2+p+7p2+4p−5
- Answer
-
p+3p+5
14. 5q2+3q−9q2+6q+8−4q2+9q+7q2+6q+8
15. 5r2+7r−33r2−49−4r2+5r+30r2−49
- Answer
-
r+9r+7
16. 7t2−t−4t2−25−6t2+12t−44t2−25
Add and Subtract Rational Expressions whose Denominators are Opposites
In the following exercises, add or subtract.
17. 10v2v−1+2v+41−2v
- Answer
-
4
18. 20w5w−2+5w+62−5w
19. 10x2+16x−78x−3+2x2+3x−13−8x
- Answer
-
x+2
20. 6y2+2y−113y−7+3y2−3y+177−3y
21. z2+6zz2−25−3z+2025−z2
- Answer
-
z+4z−5
22. a2+3aa2−9−3a−279−a2
23. 2b2+30b−13b2−49−2b2−5b−849−b2
- Answer
-
4b−3b−7
24. c2+5c−10c2−16−c2−8c−1016−c2
Find the Least Common Denominator of Rational Expressions
In the following exercises, a. find the LCD for the given rational expressions b. rewrite them as equivalent rational expressions with the lowest common denominator.
25. 5x2−2x−8,2xx2−x−12
- Answer
-
a. (x+2)(x−4)(x+3)
b. 5x+15(x+2)(x−4)(x+3),
2x2+4x(x+2)(x−4)(x+3)
26. 8y2+12y+35,3yy2+y−42
27. 9z2+2z−8,4zz2−4
- Answer
-
a. (z−2)(z+4)(z−4)
b. 9z−36(z−2)(z+4)(z−4),
4z2−8z(z−2)(z+4)(z−4)
28. 6a2+14a+45,5aa2−81
29. 4b2+6b+9,2bb2−2b−15
- Answer
-
a. (b+3)(b+3)(b−5)
b. 4b−20(b+3)(b+3)(b−5),
2b2+6b(b+3)(b+3)(b−5)
30. 5c2−4c+4,3cc2−7c+10
31. 23d2+14d−5,5d3d2−19d+6
- Answer
-
a. (d+5)(3d−1)(d−6)
b. 2d−12(d+5)(3d−1)(d−6),
5d2+25d(d+5)(3d−1)(d−6)
32. 35m2−3m−2,6m5m2+17m+6
Add and Subtract Rational Expressions with Unlike Denominators
In the following exercises, perform the indicated operations.
33. 710x2y+415xy2
- Answer
-
21y+8x30x2y2
34. 112a3b2+59a2b3
35. 3r+4+2r−5
- Answer
-
5r−7(r+4)(r−5)
36. 4s−7+5s+3
37. 53w−2+2w+1
- Answer
-
11w+1(3w−2)(w+1)
38. 42x+5+2x−1
39. 2yy+3+3y−1
- Answer
-
2y2+y+9(y+3)(y−1)
40. 3zz−2+1z+5
41. 5ba2b−2a2+2bb2−4
- Answer
-
b(5b+10+2a2)a2(b−2)(b+2)
42. 4cd+3c+1d2−9
43. −3m3m−3+5mm2+3m−4
- Answer
-
−mm+4
44. 84n+4+6n2−n−2
45. 3rr2+7r+6+9r2+4r+3
- Answer
-
3(r2+6r+18)(r+1)(r+6)(r+3)
46. 2ss2+2s−8+4s2+3s−10
47. tt−6−t−2t+6
- Answer
-
2(7t−6)(t−6)(t+6)
48. x−3x+6−xx+3
49. 5aa+3−a+2a+6
- Answer
-
4a2+25a−6(a+3)(a+6)
50. 3bb−2−b−6b−8
51. 6m+6−12mm2−36
- Answer
-
−6m−6
52. 4n+4−8nn2−16
53. −9p−17p2−4p−21−p+17−p
- Answer
-
p+2p+3
54. −13q−8q2+2q−24−q+24−q
55. −2r−16r2+6r−16−52−r
- Answer
-
3r−2
56. 2t−30t2+6t−27−23−t
57. 2x+710x−1+3
- Answer
-
4(8x+1)10x−1
58. 8y−45y+2−6
59. 3x2−3x−4−2x2−5x+4
- Answer
-
x−5(x−4)(x+1)(x−1)
60. 4x2−6x+5−3x2−7x+10
61. 5x2+8x−9−4x2+10x+9
- Answer
-
1(x−1)(x+1)
62. 32x2+5x+2−12x2+3x+1
63. 5aa−2+9a−2a+18a2−2a
- Answer
-
5a2+7a−36a(a−2)
64. 2bb−5+32b−2b−152b2−10b
65. cc+2+5c−2−10cc2−4
- Answer
-
c−5c+2
66. 6dd−5+1d+4+7d−5d2−d−20
67. 3dd+2+4d−d+8d2+2d
- Answer
-
3(d+1)d+2
68. 2qq+5+3q−3−13q+15q2+2q−15
Add and Subtract Rational Functions
In the following exercises, find a. R(x)=f(x)+g(x) b. R(x)=f(x)−g(x).
69. f(x)=−5x−5x2+x−6 and g(x)=x+12−x
- Answer
-
a. R(x)=−(x+8)(x+1)(x−2)(x+3)
b. R(x)=x+1x+3
70. f(x)=−4x−24x2+x−30 and g(x)=x+75−x
71. f(x)=6xx2−64 and g(x)=3x−8
- Answer
-
a. R(x)=3(3x+8)(x−8)(x+8)
b. R(x)=3x+8
72. f(x)=5x+7 and g(x)=10xx2−49
Writing Exercises
73. Donald thinks that 3x+4x is 72x. Is Donald correct? Explain.
- Answer
-
Answers will vary.
74. Explain how you find the Least Common Denominator of x2+5x+4 and x2−16.
75. Felipe thinks 1x+1y is 2x+y.
a. Choose numerical values for x and y and evaluate 1x+1y.
b. Evaluate 2x+y for the same values of x and y you used in part a..
c. Explain why Felipe is wrong.
d. Find the correct expression for 1x+1y.
- Answer
-
a. Answers will vary.
b. Answers will vary.
c. Answers will vary.
d. x+yx
76. Simplify the expression 4n2+6n+9−1n2−9 and explain all your steps.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all objectives?