Chapter 3
Section 3.1: Reducing Fractions
1. $\tfrac{2x}{3y}$ 3. $\tfrac{4{{b}^{2}}}{{{a}^{2}}}$ 5. $\tfrac{2{{K}^{2}}+5}{3K}$ 7. $\tfrac{x+3}{4x-1}$ 9. $\tfrac{2x-3}{3x-2}$ 11. $\tfrac{3{{a}^{2}}+4{{b}^{2}}}{2b}$
13. Doesn't reduce 15. $\tfrac{4x}{x+4}$ 17. $\tfrac{x+1}{2(x+7)}$ 19. $\tfrac{x-2}{3(x-8)}$ 21. $\tfrac{x-1}{x+6}$
23. $-\tfrac{x}{y}$ 25. $\tfrac{x+y}{x+1}$ 27. $\tfrac{x+3+K}{x+3-K}$ 29. $-\tfrac{6x-1}{2x-1}$ 31. $\tfrac{1}{5(x-2)(x+1)}$ 33. $\tfrac{(x-2)(x-1)}{(x+2)(x+1)}$
35. $-(x-2)$ 37. $(x+3)(x+2)$ 39. $\tfrac{3-x}{(x+1)(x+2)}$ 41. $\tfrac{x+2y}{a+b}$ 43. $\tfrac{x-a}{3a+2b}$
45. $\tfrac{(x+2)(x-2)}{(x+4)(x-4)}$ 47. $-\tfrac{x+2}{x+1}$ 49. $\tfrac{2x+5}{3x+4}$ 51. $\tfrac{2(1-2y)}{3}$ 53. $\tfrac{x+6}{x-6}$ 55. $\tfrac{6x}{x-5}$
Section 3.2: Multiplying and Dividing Fractions
1. $\tfrac{5}{2}$ 3. $\tfrac{2xy}{27}$ 5. $-\tfrac{2(x+4)}{x-2}$ 7. $-\tfrac{8}{k+8}$ 9. $-\tfrac{x}{x+3}$
11. $\tfrac{x-3}{x+4}$ 13. $1$ 15. $\tfrac{a-2}{a}$ 17. $-2(2x-1)$
Section 3.3: Adding Fractions
1. $\tfrac{x}{2}$ 3. $-2$ 5. $-\tfrac{29}{18t}$ 7. $\tfrac{{{x}^{2}}+4xy+{{y}^{2}}}{{{x}^{2}}{{y}^{2}}}$ 9. $\tfrac{2{{x}^{2}}-10x+25}{x(x-5)}$ 11. $-\tfrac{7x+13}{4x}$
13. $\tfrac{3{{y}^{2}}+13xy-6{{x}^{2}}}{2{{x}^{2}}{{y}^{2}}}$ 15. $\tfrac{{{x}^{2}}+2x-9}{(x-2)(x-4)(x+1)}$ 17. $\tfrac{5x+7}{(x+3){{(x-1)}^{2}}}$ 19. $\tfrac{{{x}^{2}}+2}{x}$
21. 23. 25. 27. 29.
31. $-\tfrac{3}{4ab}$ 33. $\tfrac{{{x}^{2}}+3x+y}{xy}$ 35. $-\tfrac{x-3}{(x+3)(x+1)}$ 37. $\tfrac{2}{(x+1)(x-1)}$ 39. $-\tfrac{x-2}{x-1}$
41. $\tfrac{3x-5}{(x-1)(x-2)(x-3)}$ 43. $\tfrac{2}{(x+1)(x+2)(x+3)}$ 45. $\tfrac{x-5}{(x-1)(x-3)}$ 47. $\tfrac{-11}{x+3}$
49. $\tfrac{1}{x}$ 51. $\tfrac{5}{x-2}$ 53. $\tfrac{9{{a}^{2}}+7a+5}{(a-1)(a+2)(a+3)}$ 55. $\tfrac{2x-8}{(x-1)(x-2)(x+3)}$
57. $\tfrac{{{x}^{2}}+1}{{{x}^{2}}-1}$ 59. $\tfrac{{{x}^{2}}+{{a}^{2}}}{{{x}^{2}}-{{a}^{2}}}$ 61. $\tfrac{2}{(x-1)(x-2)(x+3)}$ 63. $\tfrac{{{x}^{2}}-9x+24}{(x-3)(x-5)}$ 65. $\tfrac{-{{x}^{2}}+x+8}{(x+1)(x-1)}$
Section 3.4: Linear Equations 2
1. 30 3. 2 5. 3 7. All real numbers except $x=-2$
9. ${\scriptstyle{}^{5}\!\!\diagup\!\!{}_{2}\;}$ 11. ${\scriptstyle{}^{35}\!\!\diagup\!\!{}_{6}\;}$ 13. 2 15. ${\scriptstyle{}^{(a-1)}\!\!\diagup\!\!{}_{5}\;}$ 17. ${\scriptstyle{}^{(4a+1)}\!\!\diagup\!\!{}_{6}\;}$ 19. a
Section 3.5: Averages
1. 88 3. 95% 5. 76% 7. 90 at-bats; 36 hits
9. 30 11. a. 50 mph b. 48 mph c. 40 minutes 13. 10
Section 3.6: Complex Fractions
1. $\tfrac{x}{1-2x}$ 3. $\tfrac{ab}{b-2a}$ 5. $\tfrac{2x-3}{3x-1}$ 7. $\tfrac{6}{5}$ 9. $\tfrac{3m-1}{{{m}^{2}}-9}$ 11. $-(x+y)$
13. $\tfrac{1}{2x}$ 15. $\tfrac{x-1}{x}$ 17. $\tfrac{2x+y}{x}$ 19. $\tfrac{-x+2}{2x-1}$ 21. $\tfrac{1}{x}$
Section 3.7: Miscellaneous Fraction Problems
1. $\tfrac{bc+2ac-3ab}{abc}$ 3. $\tfrac{5}{(x-2)(x+3)}$ 5. $\tfrac{x-8}{2x-1}$ 7. $-\tfrac{x+2}{4}$ 9. $\tfrac{y-2}{y}$
11. $\tfrac{{{x}^{2}}}{3(x+9)}$ 13. $\tfrac{28ab-24ac+9bc}{12{{a}^{2}}{{b}^{2}}{{c}^{2}}}$ 15. $\tfrac{{{(x-2)}^{2}}}{x-4}$ 17. $\tfrac{{{a}^{2}}-a+1}{a(a-1)}$ 19. $\tfrac{x+9}{(x-3)(x+1)}$
21. $\tfrac{6-2x}{x+12}$ 23. 12 mph 25. a. $-32$ b. $-7,\ \ 5$