# Honors Algebra 2: Extra Practice on Adding and Subtracting Rational Expressions

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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1. $$\displaystyle \frac{ 5x}{8} + \frac{3x}{2} + \frac{ x }{ 4 }$$
2. Solution

$$\displaystyle \frac{ 19x}{ 8}$$

3. $$\displaystyle \frac{ 3m}{7} + \frac{ m }{ 14 } + \frac{ 5m }{ 2 }$$
4. Solution

$$\displaystyle 3m$$

5. $$\displaystyle \frac{ 3x - 5 }{ 6 } + \frac{ 2x + 1 }{ 4 }$$
6. Solution

$$\displaystyle \frac{ 12x - 7}{ 12}$$

7. $$\displaystyle \frac{ 4y - 1 }{ 5 } + \frac{ y }{ 10 } + \frac{ 3y - 2 }{ 6 }$$
8. Solution

$$\displaystyle \frac{ 21y - 8}{ 15}$$

9. $$\displaystyle \left( \frac{ 2a }{ 3 } + \frac{ 1 }{ 6 } \right) \div \frac{ 16a^2 - 1 }{ 12 }$$
10. Solution

$$\displaystyle \frac{ 2}{ 4a - 1}$$

11. $$\displaystyle \frac{ 3x - 2 }{ x^2 - 5x } + \frac{ 4 }{ x^2 - 7x + 10 }$$
12. Solution

$$\displaystyle \frac{ 3x^2 - 4x + 4}{ x(x - 5)(x - 2)}$$

13. $$\displaystyle \frac{ 6k - 22 }{ k^2 - 5k + 6 } +\frac{ k + 1 }{ k - 3 }$$
14. Solution

$$\displaystyle \frac{ k + 8}{ k - 2} , k \ne 3$$

15. $$\displaystyle \frac{ 5 }{ a } + 6$$
16. Solution

$$\displaystyle \frac{ 6a + 5}{ a}$$

17. $$\displaystyle 9 + \frac{ 4 }{ m }$$
18. Solution

$$\displaystyle \frac{ 9m + 4}{ m}$$

19. $$\displaystyle \frac{ 7 }{ a - 3 } + \frac{ 4 }{ a + 6 }$$
20. Solution

$$\displaystyle \frac{ 11a + 30}{ (a - 3)(a + 6)}$$

21. $$\displaystyle \frac{ 3 }{ b - 4 }+ \frac{ 2 }{ b + 5 }$$
22. Solution

$$\displaystyle \frac{ 5b + 7}{ (b - 4)(b + 5)}$$

23. $$\displaystyle \frac{ 7 }{ 2a } + \frac{ 2a }{ 3a^2 } + \frac{ 3+5a }{ 6a^3 }$$
24. Solution

$$\displaystyle \frac{ 19a^2 + 9a + 3}{ 6a^3}$$

25. $$\displaystyle x - 5 + \frac{ 7 }{ 3x + 2 }$$
26. Solution

$$\displaystyle \frac{ 3x^2 - 13x - 3}{ 3x + 2}$$

27. $$\displaystyle \frac{ 4 }{ a - 2 } + \frac{ 3 }{ a - 1 } + \frac{ 2}{ a + 1 }$$
28. Solution

$$\displaystyle \frac{ 9a^2 - 9a - 6}{ (a - 2)(a - 1)(a + 1)}$$

29. $$\displaystyle \frac{ 6 }{ x - 5 }- \frac{ x - 3 }{ x^2 - 25 }$$
30. Solution

$$\displaystyle \frac{ 5x + 33}{ (x + 5)(x - 5)}$$

31. $$\displaystyle \frac{ 5 }{ 3b - 2 } - \frac{ 4 }{ 2b + 5 }$$
32. Solution

$$\displaystyle \frac{ -2b + 33}{ (3b - 2)(2b + 5)}$$

33. $$\displaystyle \frac{ 7 }{ 12y^3 } - \frac{ 3 }{ 8y^2 }$$
34. Solution

$$\displaystyle \frac{ 14 - 9y}{ 24y^3}$$

35. $$\displaystyle \frac{ 2 }{ 9m^2 }- \frac{ 5 }{ 3m }$$
36. Solution

$$\displaystyle \frac{ 2 - 15m}{ 9m^2}$$

37. $$\displaystyle \frac{ 5 }{ k^2 - 5k - 24 } - \frac{ 2 }{ k - 8 }$$
38. Solution

$$\displaystyle -\frac{ 2x + 1)}{ (k - 8)(x + 3)}$$

39. $$\displaystyle \frac{ 5 }{ k^2 - 5k - 14 } - \frac{k - 1}{k - 7}$$
40. Solution

$$\displaystyle -\frac{ k^2 + k - 7}{ (k - 7)(k + 2)}$$

41. $$\displaystyle \frac{ 4 }{ xy - 3x + ay - 3a } - \frac{ a + 1 }{ y^2 + y - 12 }$$
42. Solution

$$\displaystyle \frac{ 4y + 16 - xa - x - a^2 - a}{ (x + a)(y - 3)(y + 4)}$$

43. $$\displaystyle \frac{ 3 }{ xy - 3xb + 2y^2 - 6yb }- \frac{ 7 }{ y^2 - 9b^2 }$$
44. Solution

$$\displaystyle \frac{ -11y+9b-7k}{ (x + 2y)(y - 3b)(y + 3b)}$$

45. $$\displaystyle \frac{ 4a }{ a^2 - 9 } + \frac{2}{3 - a}$$
46. Solution

$$\displaystyle \frac{ 2}{ a + 3} , a \ne 3$$

47. $$\displaystyle \frac{ 5y + 2 }{ y^2 - 4y - 12 } + \frac{ 4 }{ 6 - y }$$
48. Solution

$$\displaystyle \frac{ 1}{ y + 2} , y \ne 6$$

49. $$\displaystyle \frac{ 18 - 17b }{ b^2 + 2b - 48 } - \frac{ b }{ 6 - b }$$
50. Solution

$$\displaystyle \frac{ b - 3}{ b + 8} , b \ne 6$$

51. $$\displaystyle \frac{ 4 }{ m - 8 } + \frac{ 3 }{ 4 - m }$$
52. Solution

$$\displaystyle \frac{ m + 8}{ (m - 8)(m - 4)}$$

53. $$\displaystyle \frac{ 3 }{ t } - \frac{ 7 - t }{ 2t - t^2 }$$
54. Solution

$$\displaystyle \frac{ 2t + 1}{ t(t - 2)}$$

55. $$\displaystyle \frac{ 9y - 22 }{ y^2 - 2y } - \frac{ y }{ 2 - y }$$
56. Solution

$$\displaystyle \frac{ y + 11}{ y}, y \ne 2$$