For f ( x ) = 8 x , g ( x ) = 1 x , f open x close equals 8 x comma . g open x close equals , 1 over x . comma  and h ( x ) = 1 x − 5 , h open x close equals . fraction 1 , over x minus 5 end fraction . comma  perform the indicated operation.

Example f ( x ) ÷ g ( x ) = 8 x ÷ 1 x = 8 x ⋅ x 1 = 8 x 2 f open x close divides g open x close equals 8 x divides , 1 over x , equals 8 x dot , x over 1 , equals 8 , x squared

45. f ( x ) + g ( x ) f open x close plus g open x close
46. f ( x ) · g ( x ) f open x close middle dot g open x close
47. g ( x ) − h ( x ) g open x close minus h open x close
48. h ( x ) ÷ f ( x ) h open x close divides f open x close

C Challenge

Simplify each complex fraction.

49. 3 + x 2 2 + x 3 fraction 3 plus , x over 2 , over 2 plus , x over 3 end fraction
50. x + y 1 + x y fraction x plus y , over 1 plus , x over y end fraction
51. − 4 3 x + y fraction negative 4 , over 3 over x , plus y end fraction
52. 1 x − 4 x 3 y + 5 y fraction 1 over x , minus , 4 over x , over 3 over y , plus , 5 over y end fraction
53. 3 x + 4 y 2 x − 3 y fraction 3 over x , plus , 4 over y , over 2 over x , minus , 3 over y end fraction
54. 7 c + 1 + 4 3 − 2 c + 1 fraction fraction 7 , over c plus 1 end fraction . plus 4 , over 3 minus . fraction 2 , over c plus 1 end fraction end fraction

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

55. What is the difference 3 x 3 x − 2 − 2 3 x − 2 fraction 3 x , over 3 x minus 2 end fraction . minus . fraction 2 , over 3 x minus 2 end fraction  when x ≠ 2 3 ? x not equal to , 2 thirds , question mark

56. The area of the figure shown below is 200 cm 2 . 200 , cm squared , .  What is the value of x to the nearest hundredth of a centimeter?

    

57. A band director can line up the band members in equal rows of 4, 5, or 8. What is the least number of band members?
58. The members of a bicycle club rode a 20-mi round-trip route. On the way back, they had a tailwind and averaged 3 mi/h faster than on the first half of the trip. Suppose the bicyclists averaged a rate of 12 mi/h for the first half of the trip. How many hours did the round trip take?

Mixed Review

See Lesson 11-3.

Divide.

59. ( 2 x 4 + 8 x 3 − 4 x 2 ) ÷ 4 x 2 open 2 , x to the fourth , plus 8 , x cubed , minus 4 , x squared , close divides 4 , x squared
60. ( 10 b + 5 b 2 ) ÷ ( b + 2 ) open 10 b plus 5 , b squared , close divides open b plus 2 close
61. ( y 4 − y 2 ) ÷ ( y 2 − 2 y − 3 ) open , y to the fourth , minus , y squared , close divides open , y squared , minus 2 y minus 3 close

See Lesson 10-4.

Solve each radical equation. Check your answers. If there is no solution, write no solution.

62. x = 5 x + 6 x equals . square root of 5 x plus 6 end root
63. n = 24 − 5 n n equals . square root of 24 minus 5 n end root
64. 16 y = − 8 square root of 16 y end root , equals negative 8

Get Ready! To prepare for Lesson 11-5, do Exercises 65–67.

See Lesson 2-7.

Solve each proportion.

65. 1 x = 3 5 1 over x , equals , 3 fifths
66. 3 t = 5 2 3 over t , equals , 5 halves
67. m 3 = 17 51 m over 3 , equals , 17 over 51

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