Algebra-Trigonometry-CynthiaYoung-3ed10.pdf - c00c.qxd 4:31 PM Page 61 0.5 Rational Expressions 61 In Exercises 4966 divide the rational expressions and

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0.5 Rational Expressions 61 In Exercises 49–66, divide the rational expressions and simplify. State any real numbers that must be excluded from the domain. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. In Exercises 67–82, add or subtract the rational expression and simplify. State any real numbers that must be excluded from the domain. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. In Exercises 83–90, simplify the complex rational expressions. State any real numbers that must be excluded from the domain. 83. 84. 85. 86. 87. 88. 89. 90. 3 x + 1 - 3 x - 1 5 x 2 - 1 1 x - 1 + 1 1 x + 1 + 1 7 y + 7 1 y + 7 - 1 y 1 x - 1 + 1 1 - 1 x + 1 1 x + 2 x 2 9 x - 5 x 2 3 + 1 x 9 - 1 x 2 3 y - 5 4 - 2 y 1 x - 1 1 - 2 x 3 5 y + 6 - 4 y - 2 + y 2 - y 5 y 2 - 4 y - 12 7 + 1 x - 3 1 y + 4 y 2 - 4 - 2 y 2 - 2 y 5 a a 2 - b 2 - 7 b - a 2 y - 3 + 7 y + 2 x - 1 x - 2 + x - 6 x 2 - 4 x - 1 4 - x 2 - x + 1 2 + x 3 x x 2 - 4 + 3 + x x + 2 3 1 - x + 4 x - 1 3 y 2 y + 1 + 1 - 2 y y - 1 7 2 x - 1 - 5 1 - 2 x 2 x + 1 5 x - 1 - 3 - 2 x 1 - 5 x 4 9 + x - 5 x x - 2 3 p - 2 + 5 p p + 1 5 7 x - 3 x 3 x - 2 5 x x 2 - 6 x - 27 2 x 2 + 13 x - 7 , 2 x 2 - 15 x - 27 2 x 2 + 9 x - 5 20 x 2 - 3 x - 2 25 x 2 - 4 , 12 x 2 + 23 x + 5 3 x 2 + 5 x 2 y 2 - 5 y - 3 2 y 2 - 9 y - 5 , 3 y - 9 y 2 - 5 y x 2 + 4 x - 21 x 2 + 3 x - 10 , x 2 - 2 x - 63 x 2 + x - 20 y 2 - 3 y 2 y , y 3 - 3 y 2 8 y w 2 - w w , w 3 - w 5 w 3 x 3 + 8 x 2 + 12 x 5 x 2 - 10 x , 4 x + 8 x 2 - 4 3 t 3 - 6 t 2 - 9 t 5 t - 10 , 6 + 6 t 4 t - 8 49 - y 2 y 2 - 25 , 7 + y 2 y + 10 36 - n 2 n 2 - 9 , n + 6 n + 3 4 - x x 2 - 16 , 12 - 3 x x - 4 2 - p p 2 - 1 , 2 p - 4 p + 1 5 3 x - 4 , 10 9 x 2 - 16 1 x - 1 , 5 x 2 - 1 5( x + 6) 10( x - 6) , 20( x + 6) 8 6 x - 2 , 12 ( x - 2)( x + 2) 5 x 2 , 10 x 3 3 x , 12 x 2 93. Circuits. If two resistors are connected in parallel, the combined resistance is given by the formula where R 1 and R 2 are the individual resistances. Simplify the formula. 94. Optics. The focal length of a lens can be calculated by applying the formula , where p is the distance that the object is from the lens and q is the distance that the image is from the lens. Simplify the formula. f = 1 1/ p + 1/ q R = 1 1/ R 1 + 1/ R 2 , 91. Finance. The amount of payment made on a loan is given by the formula , where p is the principal (amount borrowed), and , where r is the interest rate expressed as a decimal and n is the number of payments per year. Suppose n 5. Simplify the formula as much as possible. 92. Finance. Use the formula to calculate the amount your monthly payment will be on a loan of $150,000 at an interest rate of 6.5% for 30 years ( nt 360). A = pi 1 - 1 (1 + i ) nt i = r n A = pi 1 - 1/(1 + i ) n A P P L I C AT I O N S
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62 CHAPTER 0 Prerequisites and Review 95. Simplify . Solution: Factor the numerator. Cancel the common factor, x 1. Write in simplified form. This is incorrect. What mistake was made? = x + 1 = ( x + 1)( x + 1) ( x + 1) x 2 + 2 x + 1 x + 1 = ( x + 1)( x + 1) ( x + 1) x 2 + 2 x + 1 x + 1 96. Simplify . Solution: Cancel the common 1s. Factor the denominator. Cancel the common x . Write in simplified form. , This is incorrect. What mistake was made? x Z 0 x Z - 2 = 1 x + 2 = x x ( x + 2) = x x ( x + 2) x + 1 x 2 + 2 x + 1 x + 1 x 2 + 2 x + 1 In Exercises 97–100, determine whether each of the statements is true or false.
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