Solutions to Try Its

1. $\frac{1}{x+6}$

2. $\frac{\left(x+5\right)\left(x+6\right)}{\left(x+2\right)\left(x+4\right)}$

3. $1$

4. $\frac{2\left(x - 7\right)}{\left(x+5\right)\left(x - 3\right)}$

5. $\frac{{x}^{2}-{y}^{2}}{x{y}^{2}}$

Solutions to Odd-Numbered Exercises

1. You can factor the numerator and denominator to see if any of the terms can cancel one another out.

3. True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.

5. $\frac{y+5}{y+6}$

7. $3b+3$

9. $\frac{x+4}{2x+2}$

11. $\frac{a+3}{a - 3}$

13. $\frac{3n - 8}{7n - 3}$

15. $\frac{c - 6}{c+6}$

17. $1$

19. $\frac{{d}^{2}-25}{25{d}^{2}-1}$

21. $\frac{t+5}{t+3}$

23. $\frac{6x - 5}{6x+5}$

25. $\frac{p+6}{4p+3}$

27. $\frac{2d+9}{d+11}$

29. $\frac{12b+5}{3b - 1}$

31. $\frac{4y - 1}{y+4}$

33. $\frac{10x+4y}{xy}$

35. $\frac{9a - 7}{{a}^{2}-2a - 3}$

37. $\frac{2{y}^{2}-y+9}{{y}^{2}-y - 2}$

39. $\frac{5{z}^{2}+z+5}{{z}^{2}-z - 2}$

41. $\frac{x+2xy+y}{x+xy+y+1}$

43. $\frac{2b+7a}{a{b}^{2}}$

45. $\frac{18+ab}{4b}$

47. $a-b$

49. $\frac{3{c}^{2}+3c - 2}{2{c}^{2}+5c+2}$

51. $\frac{15x+7}{x - 1}$

53. $\frac{x+9}{x - 9}$

55. $\frac{1}{y+2}$

57. $4$