9. ${\displaystyle \frac{A}{x-1}}+{\displaystyle \frac{B}{x+2}}$

11. ${\displaystyle \frac{A}{x+6}}+{\displaystyle \frac{B}{x+1}}$

13. ${\displaystyle \frac{A}{x^2}}+{\displaystyle \frac{B}{x}}+{\displaystyle \frac{C}{x-1}}$

15. ${\displaystyle \frac{A}{x+1}}+{\displaystyle \frac{Bx+C}{x^2-x+1}}$

17. ${\displaystyle \frac{Ax+B}{x^2+1}}+{\displaystyle \frac{Cx+D}{{(x^2+1)}^2}}$

19. ${\displaystyle \frac{3}{x+2}}-{\displaystyle \frac{1}{x+1}}$

21. ${\displaystyle \frac{-1}{2(x+3)}}+{\displaystyle \frac{1}{2(x+1)}}$

23. ${\displaystyle \frac{-1}{x+2}}+{\displaystyle \frac{1}{x}}$

25. ${\displaystyle \frac{2}{x+2}}-{\displaystyle \frac{3}{2(x+3)}}-{\displaystyle \frac{1}{2(x+1)}}$

27. ${\displaystyle \frac{16}{15(x+4)}}+{\displaystyle \frac{1}{10(x-1)}}-{\displaystyle \frac{1}{6(x+1)}}$

29. ${\displaystyle \frac{1}{{(x+3)}^2}}-{\displaystyle \frac{1}{4(x+3)}}+{\displaystyle \frac{1}{4(x-5)}}$

31. ${\displaystyle \frac{-1}{x+2}}+{\displaystyle \frac{3}{{(x+2)}^2}}+{\displaystyle \frac{1}{x-3}}$

33. ${\displaystyle \frac{-2}{{(x+1)}^2}}+{\displaystyle \frac{1}{x+1}}$

35. ${\displaystyle \frac{1}{2(2x-3)}}+{\displaystyle \frac{1}{2{(2x-3)}^2}}$

37. ${\displaystyle \frac{2}{x+1}}-{\displaystyle \frac{3}{{(x+1)}^2}}+{\displaystyle \frac{1}{{(x+1)}^3}}$

39. ${\displaystyle \frac{2}{{(x+2)}^2}}-{\displaystyle \frac{1}{{(x+2)}^3}}$

41. ${\displaystyle \frac{1}{x}}+{\displaystyle \frac{3}{{(x+1)}^2}}-{\displaystyle \frac{2}{x+1}}$

43. ${\displaystyle \frac{1}{x-1}}-{\displaystyle \frac{1}{x+1}}+{\displaystyle \frac{1}{{(x+1)}^2}}$

45. ${\displaystyle \frac{-2}{x}}+{\displaystyle \frac{1}{x^2}}+{\displaystyle \frac{1}{{(x+1)}^2}}+{\displaystyle \frac{2}{x+1}}$

47. ${\displaystyle \frac{1}{4{(x-1)}^2}}+{\displaystyle \frac{1}{4{(x+1)}^2}}+{\displaystyle \frac{1}{4(x+1)}}-{\displaystyle \frac{1}{4(x-1)}}$

49. ${\displaystyle \frac{2}{3}}\left({\displaystyle \frac{2x+3}{x^2-2x+3}}\right)-{\displaystyle \frac{1}{3(x-2)}}$

51. ${\displaystyle \frac{1}{x+1}}-{\displaystyle \frac{2}{{(x+1)}^2}}+{\displaystyle \frac{1-x}{x^2+2x+2}}$

53. ${\displaystyle \frac{-1}{x-2}}+{\displaystyle \frac{5}{{(x-2)}^2}}+{\displaystyle \frac{2}{x-1}}$

55. ${\displaystyle \frac{-2}{{(2x+3)}^2}}+{\displaystyle \frac{3}{2x+3}}$

57. ${\displaystyle \frac{4}{x}}-{\displaystyle \frac{3}{x^2}}-{\displaystyle \frac{4}{x+1}}$

59. ${\displaystyle \frac{-2}{x}}+{\displaystyle \frac{3}{x+1}}+{\displaystyle \frac{4}{x^2}}$

61. ${\displaystyle \frac{-x}{2(x^2+1)}}+{\displaystyle \frac{1}{4(x+1)}}+{\displaystyle \frac{1}{4(x-1)}}$

63. ${\displaystyle \frac{-x}{x^2+1}}+{\displaystyle \frac{1}{x}}-{\displaystyle \frac{x}{{(x^2+1)}^2}}$

65. ${\displaystyle \frac{4-3x}{x^2+2}}+{\displaystyle \frac{-2+3x}{x^2+1}}$