81 R.7 Rational Expressions 67. 4 x + 1 + 1 x2 - x + 1 - 12 x3 + 1 68. 5 x + 2 + 2 x2 - 2x + 4 - 60 x3 + 8 69. 3x x2 + x - 12 - x x2 - 16 70. p 2p2 - 9p - 5 - 2p 6p2 - p - 2 Simplify each complex fraction. See Example 5. 71. 1 + 1 x 1 - 1 x 72. 2 - 2 y 2 + 2 y 73. 1 x + 1 - 1 x 1 x 74. 1 y + 3 - 1 y 1 y 75. 1 + 1 1 - b 1 - 1 1 + b 76. 2 + 2 1 + x 2 - 2 1 - x 77. 1 a3 + b3 1 a2 + 2ab + b2 78. 1 x3 - y3 1 x2 - y2 79. m1 m2 - 4 1 m+ 2 80. y + 1 y2 - 9 1 y + 3 81. 3 p2 - 16 + p 1 p - 4 82. 6 x2 - 25 + x 1 x - 5 83. y + 3 y - 4 y - 1 y y - 1 + 1 y 84. x + 4 x - 3 x - 2 x x - 2 + 1 x 85. 1 x + h - 1 x h 86. -2 x + h - -2 x h 87. 1 1x + h22 + 9 - 1 x2 + 9 h 88. 2 1x + h22 + 16 - 2 x2 + 16 h Perform all indicated operations, and write each answer with positive integer exponents. See Example 6. 89. a-1 + b-1 1ab2-1 90. p-1 - q-1 1pq2-1 91. r-1 + q-1 r-1 - q-1 # r - q r + q 92. x-2 + y-2 x-2 - y-2 # x + y x - y 93. x - 9y-1 1x - 3y-121x + 3y-12 94. a - 16b-1 1a + 4b-121a - 4b-12 Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) 95. 1x2 + 12412x2 - x21421x2 + 12312x2 1x2 + 128 96. 1y2 + 22513y2 - y31621y2 + 22413y2 1y2 + 227
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