Practice and Problem-Solving Exercises

A Practice

See Problems 1, 2, and 3.

Multiply.

11. 7 3 ⋅ 5 x 12 7 thirds , dot , fraction 5 x , over 12 end fraction
12. 3 t ⋅ 4 t 3 over t , dot , 4 over t
13. 5 3 a 2 ⋅ 8 a 3 fraction 5 , over 3 , eh squared end fraction . dot , fraction 8 , over eh cubed end fraction
14. m − 2 m + 2 ⋅ m m − 1 fraction m minus 2 , over m plus 2 end fraction . dot . fraction m , over m minus 1 end fraction
15. 2 x x + 1 ⋅ x − 1 3 fraction 2 x , over x plus 1 end fraction . dot . fraction x minus 1 , over 3 end fraction
16. 6 x 2 5 ⋅ 2 x + 1 fraction 6 , x squared , over 5 end fraction . dot . fraction 2 , over x plus 1 end fraction
17. 4 c 2 c + 2 ⋅ c 2 + 3 c + 2 c − 1 fraction 4 c , over 2 c plus 2 end fraction . dot . fraction c squared , plus 3 c plus 2 , over c minus 1 end fraction
18. b 2 + 4 b + 4 2 b 2 − 8 ⋅ 3 b − 6 4 b fraction b squared , plus 4 b plus 4 , over 2 , b squared , minus 8 end fraction . dot . fraction 3 b minus 6 , over 4 b end fraction
19. r 2 + 5 r + 6 2 r ⋅ r − 2 r + 3 fraction r squared , plus 5 r plus 6 , over 2 r end fraction . dot . fraction r minus 2 , over r plus 3 end fraction
20. m − 2 3 m + 9 ⋅ 2 m + 6 2 m − 4 fraction m minus 2 , over 3 m plus 9 end fraction . dot . fraction 2 m plus 6 , over 2 m minus 4 end fraction
21. t 2 − t − 12 t + 1 ⋅ t + 1 t + 3 fraction t squared , minus t minus 12 , over t plus 1 end fraction . dot . fraction t plus 1 , over t plus 3 end fraction
22. 4 x + 1 5 x + 10 ⋅ 30 x + 60 2 x − 2 fraction 4 x plus 1 , over 5 x plus 10 end fraction . dot . fraction 30 x plus 60 , over 2 x minus 2 end fraction
23. 4 t + 4 t − 3 . ( t 2 − t − 6 ) fraction 4 t plus 4 , over t minus 3 end fraction . . open , t squared , minus t minus 6 close
24. 2 m + 1 3 m − 6 ⋅ ( 9 m 2 − 36 ) fraction 2 m plus 1 , over 3 m minus 6 end fraction . dot open 9 , m squared , minus 36 close
25. ( x 2 − 1 ) ⋅ x − 2 3 x + 3 open , x squared , minus 1 close dot . fraction x minus 2 , over 3 x plus 3 end fraction
26. 2 y + 9 4 y + 12 ⋅ ( y 2 + y − 6 ) fraction 2 y plus 9 , over 4 y plus 12 end fraction . dot open , y squared , plus y minus 6 close
27. h − 1 6 h + 3 ⋅ ( 2 h 2 + 9 h + 4 ) fraction h minus 1 , over 6 h plus 3 end fraction . dot open 2 , h squared , plus 9 h plus 4 close
28. ( w 2 − 8 w + 15 ) ⋅ w + 3 4 w − 20 open , w squared , minus 8 w plus 15 close dot . fraction w plus 3 , over 4 w minus 20 end fraction

See Problems 4 and 5.

Find the reciprocal of each expression.

29. 2 x + 1 fraction 2 , over x plus 1 end fraction
30. − 6 d 2 2 d − 5 fraction negative 6 , d squared , over 2 d minus 5 end fraction
31. c 2 − 1 c squared , minus 1

Divide.

32. x − 1 x + 4 ⋅ x + 3 x + 4 fraction x minus 1 , over x plus 4 end fraction . dot . fraction x plus 3 , over x plus 4 end fraction
33. 3 t + 12 5 t ÷ t + 4 10 t fraction 3 t plus 12 , over 5 t end fraction . divides . fraction t plus 4 , over 10 t end fraction
34. x − 3 6 ÷ 3 − x 2 fraction x minus 3 , over 6 end fraction . divides . fraction 3 minus x , over 2 end fraction
35. y − 4 10 ÷ 4 − y 5 fraction y minus 4 , over 10 end fraction . divides . fraction 4 minus y , over 5 end fraction
36. x 2 + 6 x + 8 x 2 + x − 2 ÷ x + 4 2 x + 4 fraction x squared , plus 6 x plus 8 , over x squared , plus x minus 2 end fraction . divides . fraction x plus 4 , over 2 x plus 4 end fraction
37. 2 n 2 − 5 n − 3 4 n 2 − 12 n − 7 ÷ 4 n + 5 2 n − 7 fraction 2 , n squared , minus 5 n minus 3 , over 4 , n squared , minus 12 n minus 7 end fraction . divides . fraction 4 n plus 5 , over 2 n minus 7 end fraction
38. 3 x + 9 x ÷ ( x + 3 ) fraction 3 x plus 9 , over x end fraction . divides open x plus 3 close
39. 11 k + 121 7 k − 15 ÷ ( k + 11 ) fraction 11 k plus 121 , over 7 k minus 15 end fraction . divides open k plus 11 close
40. x 2 + 10 x − 11 x 2 + 12 x + 11 ÷ ( x − 1 ) fraction x squared , plus 10 x minus 11 , over x squared , plus 12 x plus 11 end fraction . divides open x minus 1 close

See Problem 6.

Simplify each complex fraction.

41. 4 b − 1 b 2 + 2 b + 1 12 b − 3 b 2 − 1 fraction fraction 4 b minus 1 , over b squared , plus 2 b plus 1 end fraction , over fraction 12 b minus 3 , over b squared , minus 1 end fraction end fraction
42. 3 x 2 + 2 x + 1 8 x 12 x 2 + 8 x + 4 fraction fraction 3 , x squared , plus 2 x plus 1 , over 8 x end fraction , over 12 , x squared , plus 8 x plus 4 end fraction
43. 6 s + 12 s + 2 3 fraction 6 s plus 12 , over fraction s plus 2 , over 3 end fraction end fraction
44. t 2 − t − 6 t − 3 t + 2 fraction t squared , minus t minus 6 , over fraction t minus 3 , over t plus 2 end fraction end fraction
45. x 2 − 25 x 2 + 6 x + 5 2 x − 10 fraction x squared , minus 25 , over fraction x squared , plus 6 x plus 5 , over 2 x minus 10 end fraction end fraction
46. 3 3 d 2 + 5 d − 2 3 2 d + 4 fraction fraction 3 , over 3 , d squared , plus 5 d minus 2 end fraction , over fraction 3 , over 2 d plus 4 end fraction end fraction
47. g + 2 3 g − 1 g 2 + 2 g 6 g + 2 fraction fraction g plus 2 , over 3 g minus 1 end fraction , over fraction g squared , plus 2 g , over 6 g plus 2 end fraction end fraction
48. 5 f 2 10 f f 2 + 1 fraction 5 , f squared , over fraction 10 f , over f squared , plus 1 end fraction end fraction
49. z − 10 z + 10 3 z 2 − 30 z fraction fraction z minus 10 , over z plus 10 end fraction , over 3 , z squared , minus 30 z end fraction
50. c + 4 c 2 + 5 c + 6 3 c 2 + 12 c 2 c 2 + 5 c − 3 fraction fraction c plus 4 , over c squared , plus 5 c plus 6 end fraction , over fraction 3 , c squared , plus 12 c , over 2 , c squared , plus 5 c minus 3 end fraction end fraction

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