By Ron Larson, Robert P. Hostetler
This market-leading textual content keeps to supply scholars and teachers with sound, regularly established motives of the mathematical options. Designed for a two-term direction, the recent 7th version keeps the positive factors that experience made Algebra and Trigonometry an entire resolution for either scholars and teachers: attention-grabbing purposes, state-of-the-art layout, and leading edge expertise mixed with an abundance of conscientiously written routines.
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This market-leading textual content maintains to supply scholars and teachers with sound, continuously dependent factors of the mathematical options. Designed for a two-term direction, the recent 7th version keeps the gains that experience made Algebra and Trigonometry a whole answer for either scholars and teachers: fascinating functions, state of the art layout, and cutting edge know-how mixed with an abundance of conscientiously written routines.
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63. 65. 67. 69. 71. 73. 75. 77. 79. 80. 81. 82. 83. 84. 85. 87. 89. 91. 93. 94. 95. 96. 97. 98. 99. 100. ͑x ϩ 3͒͑x ϩ 4͒ 64. ͑x Ϫ 5͒͑x ϩ 10͒ ͑3x Ϫ 5͒͑2x ϩ 1͒ 66. ͑7x Ϫ 2͒͑4x Ϫ 3͒ ͑x ϩ 10͒͑x Ϫ 10͒ 68. ͑2x ϩ 3͒͑2x Ϫ 3͒ ͑x ϩ 2y͒͑x Ϫ 2y͒ 70. ͑4a ϩ 5b͒͑4a Ϫ 5b͒ 2 ͑2x ϩ 3͒ 72. ͑5 Ϫ 8x͒ 2 ͑x ϩ 1͒ 3 74. ͑x Ϫ 2͒ 3 ͑2x Ϫ y͒ 3 76. ͑3x ϩ 2y͒ 3 3 2 ͑4x Ϫ 3͒ 78. ͑8x ϩ 3͒2 ͑x 2 Ϫ x ϩ 1͒͑x 2 ϩ x ϩ 1͒ ͑x 2 ϩ 3x Ϫ 2͒͑x 2 Ϫ 3x Ϫ 2͒ ͑Ϫx2 ϩ x Ϫ 5͒͑3x2 ϩ 4x ϩ 1͒ ͑2x2 Ϫ x ϩ 4͒͑x2 ϩ 3x ϩ 2͒ ͓͑m Ϫ 3͒ ϩ n͔͓͑m Ϫ 3͒ Ϫ n͔ ͓͑x Ϫ 3y͒ ϩ z͔͓͑x Ϫ 3y͒ Ϫ z͔ ͓͑x Ϫ 3͒ ϩ y͔2 86.
A b и c ϭ a, иc b c 0 46 Chapter P Prerequisites The key to success in simplifying rational expressions lies in your ability to factor polynomials. When simplifying rational expressions, be sure to factor each polynomial completely before concluding that the numerator and denominator have no factors in common. Example 2 WARNING / CAUTION In Example 2, do not make the mistake of trying to simplify further by dividing out terms. xϩ6 xϩ6 ϭ ϭxϩ2 3 3 Remember that to simplify fractions, divide out common factors, not terms.
Sometimes it may be necessary to change the sign of a factor by factoring out ͑Ϫ1͒ to simplify a rational expression, as shown in Example 3. Example 3 Write Simplifying Rational Expressions 12 ϩ x Ϫ x2 in simplest form. 2x2 Ϫ 9x ϩ 4 Solution 12 ϩ x Ϫ x2 ͑4 Ϫ x͒͑3 ϩ x͒ ϭ 2 2x Ϫ 9x ϩ 4 ͑2x Ϫ 1͒͑x Ϫ 4͒ ϭ Factor completely. Ϫ ͑x Ϫ 4͒͑3 ϩ x͒ ͑2x Ϫ 1͒͑x Ϫ 4͒ ϭϪ 3ϩx , x 2x Ϫ 1 4 ͑4 Ϫ x͒ ϭ Ϫ ͑x Ϫ 4͒ Divide out common factors. Now try Exercise 39. In this text, when a rational expression is written, the domain is usually not listed with the expression.