Exercises 6.4, page 198

1. $\frac{x - 6}{x - 2}$
3. $\frac{14}{21}$
5. $\frac{3 a^{2} x}{3 a y}$
7. $\frac{2 x - 4}{x^{2} + x - 6}$
9. $\frac{a x + a y}{x^{2} - y^{2}}$
11. $\frac{7}{11}$
13. $\frac{2 x y}{4 y^{2}}$
15. $\frac{4}{R + 2}$
17. $\frac{s - 5}{2 s - 1}$
19. 9xy
21. $a^{2} - 16$
23. 2x
25. 1
27. $\frac{5}{9}$
29. $\frac{3 x}{4}$
31. $\frac{1}{5 a}$
33. $\frac{2 (a - b)}{2 a - b}$
35. $\frac{4 x^{2} + 1}{(2 x + 1) (2 x - 1)}$ (cannot be reduced)
37. 3x
39. $\frac{1}{2 y^{2}}$
41. $\frac{x - 5}{x + 5}$
43. $\frac{2 w^{2} - 1}{w^{2} + 8}$
45. $\frac{5 x + 4}{x (x + 3)}$
47. $\frac{(N + 2) (N^{2} + 4)}{8}$
49. $\frac{1}{2 t + 1}$
51. $\frac{x + 3}{x - 3}$
53. $- \frac{x + y}{2}$
55. $\frac{n + 1}{n - 1}$
57. $\frac{(x + 5) (x - 3)}{(5 - x) (x + 3)}$
59. $\frac{x^{2} - x y + y^{2}}{2}$
61. $\frac{2 x}{9 x^{2} - 3 x + 1}$
63.
1. $\frac{x^{2} (x + 2)}{x^{2} + 4}$
2. $\frac{x^{2}}{(x - 2) (x + 2)}$ Numerator and denominator have no common factor. In each, $x^{2}$ is not a factor of the denominator.
65.
1. $\frac{(x - 2) (x + 1)}{x (x - 1)}$
2. $\frac{x - 2}{x}$ Numerator and denominator have no common factor. In each, x is not a factor of the numerator.
67. No ...

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans