Explanation Definition used: “The negative exponent of a number equals to the reciprocal of positive exponent of the number. That is, a − m = 1 a m ”. Result used: Method II “Step 1: Find the least common denominator among all the denominators in the complex rational expression. Step 2: Multiply both the numerator and the denominator of the complex rational expression by the least common denominator found in Step 1. Step 3: Simplify the rational expression”. Calculation: Rewrite the given expression using the definition of negative exponent as follows. x − 1 − 3 x − 2 − 9 = 1 x − 3 1 x 2 − 9 Obtain the least common denominator among all the denominators in the complex rational expression as follows. The denominators of the complex rational expression are x and x 2 . Hence, the least common denominator of the complex rational expression is x 2 . Multiply both the numerator and the denominator of the complex rational expression by the least common denominator as follows. ( 1 x − 3 ) ⋅ x 2 ( 1 x 2 − 9 ) ⋅ x 2 = 1 x ⋅ x 2 − 3 ⋅ x 2 1 x 2 ⋅ x 2 − 9 ⋅ x 2

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Question

Chapter 7.6, Problem 59E

To determine

To simplify: The complex rational expression x−1−3x−2−9.

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Chapter 7.6, Problem 58E

Chapter 7.6, Problem 60E

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For Exercises 8–10, a. Simplify the expression. Do not rationalize the denominator. b. Find the values of x for which the expression equals zero. c. Find the values of x for which the denominator is zero. 4x(4x – 5) – 2x² (4) 8. -6x(6x + 1) – (–3x²)(6) (6x + 1)2 9. (4x – 5)? - 10. V4 – x² - -() 2)

For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11

For Exercises 5–10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. 2(x + h)? + 3(x + h) · 5. (2x + 3x) 3(x + h - 4(x + h) – (3x - 4x) 6. h 1 1 1 1 (x + h) – 2 7. x - 2 2(x + h) + 5 8. 2x + 5 h (x + h) – x 9. (x + h) 10. - X h h

Chapter 7 Solutions

Elementary & Intermediate Algebra

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Prob. 68E Ch. 7.4 - Prob. 69E Ch. 7.4 - Prob. 70E Ch. 7.4 - Prob. 71E Ch. 7.4 - Prob. 72E Ch. 7.5 - The least common denominator of 18 and 518 is...Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - The first step in adding expressions with unlike...Ch. 7.5 - Prob. 5E Ch. 7.5 - Prob. 6E Ch. 7.5 - Prob. 7E Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.5 - Prob. 23E Ch. 7.5 - Prob. 24E Ch. 7.5 - Prob. 25E Ch. 7.5 - Prob. 26E Ch. 7.5 - Prob. 27E Ch. 7.5 - Prob. 28E Ch. 7.5 - Prob. 29E Ch. 7.5 - Prob. 30E Ch. 7.5 - Prob. 31E Ch. 7.5 - Prob. 32E Ch. 7.5 - Prob. 33E Ch. 7.5 - Prob. 34E Ch. 7.5 - Prob. 35E Ch. 7.5 - Prob. 36E Ch. 7.5 - Prob. 37E Ch. 7.5 - Prob. 38E Ch. 7.5 - Prob. 39E Ch. 7.5 - Prob. 40E Ch. 7.5 - Prob. 41E Ch. 7.5 - Prob. 42E Ch. 7.5 - 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Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - In Problems 14, solve the equation for the...Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7.7 - Prob. 44E Ch. 7.7 - Prob. 45E Ch. 7.7 - Prob. 46E Ch. 7.7 - Prob. 47E Ch. 7.7 - Prob. 48E Ch. 7.7 - Prob. 49E Ch. 7.7 - Prob. 50E Ch. 7.7 - Prob. 51E Ch. 7.7 - Prob. 52E Ch. 7.7 - Prob. 53E Ch. 7.7 - Prob. 54E Ch. 7.7 - Prob. 55E Ch. 7.7 - Prob. 56E Ch. 7.7 - Prob. 57E Ch. 7.7 - Prob. 58E Ch. 7.7 - Prob. 59E Ch. 7.7 - 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Prob. 9E Ch. 7.8 - Prob. 10E Ch. 7.8 - Prob. 11E Ch. 7.8 - Prob. 12E Ch. 7.8 - Prob. 13E Ch. 7.8 - To prepare for a marathon run. Sue ran 18 miles...Ch. 7.8 - Prob. 15E Ch. 7.8 - Prob. 16E Ch. 7.8 - Prob. 17E Ch. 7.8 - Prob. 18E Ch. 7.8 - Prob. 19E Ch. 7.8 - Prob. 20E Ch. 7.8 - Prob. 21E Ch. 7.8 - Prob. 22E Ch. 7.8 - In Problems 15-34, solve the proportion. See...Ch. 7.8 - Prob. 24E Ch. 7.8 - Prob. 25E Ch. 7.8 - Prob. 26E Ch. 7.8 - Prob. 27E Ch. 7.8 - Prob. 28E Ch. 7.8 - Prob. 29E Ch. 7.8 - Prob. 30E Ch. 7.8 - Prob. 31E Ch. 7.8 - Prob. 32E Ch. 7.8 - Prob. 33E Ch. 7.8 - Prob. 34E Ch. 7.8 - Prob. 35E Ch. 7.8 - Prob. 36E Ch. 7.8 - Prob. 37E Ch. 7.8 - Prob. 38E Ch. 7.8 - Prob. 39E Ch. 7.8 - Prob. 40E Ch. 7.8 - In Problems 41-44, write an algebraic expression...Ch. 7.8 - Prob. 42E Ch. 7.8 - Prob. 43E Ch. 7.8 - Prob. 44E Ch. 7.8 - Prob. 45E Ch. 7.8 - Prob. 46E Ch. 7.8 - Prob. 47E Ch. 7.8 - Prob. 48E Ch. 7.8 - Prob. 49E Ch. 7.8 - Prob. 50E Ch. 7.8 - Prob. 51E Ch. 7.8 - Prob. 52E Ch. 7.8 - Prob. 53E Ch. 7.8 - Prob. 54E Ch. 7.8 - Prob. 55E Ch. 7.8 - Prob. 56E Ch. 7.8 - Prob. 57E Ch. 7.8 - Prob. 58E Ch. 7.8 - Prob. 59E Ch. 7.8 - Prob. 60E Ch. 7.8 - Prob. 61E Ch. 7.8 - Prob. 62E Ch. 7.8 - Prob. 63E Ch. 7.8 - Prob. 64E Ch. 7.8 - Prob. 65E Ch. 7.8 - Prob. 66E Ch. 7.8 - Prob. 67E Ch. 7.8 - Prob. 68E Ch. 7.8 - Prob. 69E Ch. 7.8 - Prob. 70E Ch. 7.8 - Prob. 71E Ch. 7.8 - Prob. 72E Ch. 7.8 - Prob. 73E Ch. 7.8 - Prob. 74E Ch. 7.8 - Prob. 75E Ch. 7.8 - Prob. 76E Ch. 7.8 - Prob. 77E Ch. 7.8 - Prob. 78E Ch. 7.8 - Prob. 79E Ch. 7.8 - Prob. 80E Ch. 7.8 - Prob. 81E Ch. 7.8 - Prob. 82E Ch. 7.8 - Prob. 83E Ch. 7.8 - Prob. 84E Ch. 7.8 - Prob. 85E Ch. 7.8 - Prob. 86E Ch. 7.8 - Prob. 87E Ch. 7.8 - Prob. 88E Ch. 7.8 - A student reads the following sentence from a word...Ch. 7.8 - When modeling work problems, we assume that...Ch. 7.8 - Prob. 91E Ch. 7.8 - Explain why the following proportions all yield...Ch. 7 - Evaluate a3b3a+b when a = 2 and b = 3.Ch. 7 - Prob. 2PCT Ch. 7 - Prob. 3PCT Ch. 7 - Prob. 4PCT Ch. 7 - Prob. 5PCT Ch. 7 - Prob. 6PCT Ch. 7 - Prob. 7PCT Ch. 7 - Prob. 8PCT Ch. 7 - Prob. 9PCT Ch. 7 - Prob. 10PCT Ch. 7 - Prob. 11PCT Ch. 7 - Prob. 12PCT Ch. 7 - Prob. 13PCT Ch. 7 - Prob. 14PCT Ch. 7 - Prob. 15PCT Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - Prob. 58RE Ch. 7 - Prob. 59RE Ch. 7 - In Problems 5972, perform the indicated...Ch. 7 - Prob. 61RE Ch. 7 - Prob. 62RE Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Prob. 78RE Ch. 7 - Prob. 79RE Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE Ch. 7 - Prob. 82RE Ch. 7 - Prob. 83RE Ch. 7 - Prob. 84RE Ch. 7 - Prob. 85RE Ch. 7 - Prob. 86RE Ch. 7 - Prob. 87RE Ch. 7 - Prob. 88RE Ch. 7 - Prob. 89RE Ch. 7 - Prob. 90RE Ch. 7 - Prob. 91RE Ch. 7 - Prob. 92RE Ch. 7 - Prob. 93RE Ch. 7 - Prob. 94RE Ch. 7 - Prob. 95RE Ch. 7 - Prob. 96RE Ch. 7 - Prob. 97RE Ch. 7 - Prob. 98RE Ch. 7 - Prob. 99RE Ch. 7 - Prob. 100RE Ch. 7 - Prob. 101RE Ch. 7 - Prob. 102RE Ch. 7 - Prob. 103RE Ch. 7 - Prob. 104RE Ch. 7 - Prob. 105RE Ch. 7 - Prob. 106RE Ch. 7 - Prob. 107RE Ch. 7 - Prob. 108RE Ch. 7 - Prob. 109RE Ch. 7 - Prob. 110RE Ch. 7 - Prob. 111RE Ch. 7 - Prob. 112RE Ch. 7 - Prob. 1T Ch. 7 - Prob. 2T Ch. 7 - Prob. 3T Ch. 7 - Prob. 4T Ch. 7 - Prob. 5T Ch. 7 - Prob. 6T Ch. 7 - Prob. 7T Ch. 7 - Prob. 8T Ch. 7 - Prob. 9T Ch. 7 - Prob. 10T Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T Ch. 7 - Prob. 16T Ch. 7 - Prob. 17T Ch. 7 - Prob. 18T Ch. 7 - Prob. 19T Ch. 7 - Prob. 20T Ch. 7 - Prob. 1CUR Ch. 7 - Prob. 2CUR Ch. 7 - Prob. 3CUR Ch. 7 - Prob. 4CUR Ch. 7 - Prob. 5CUR Ch. 7 - Prob. 6CUR Ch. 7 - Prob. 7CUR Ch. 7 - Prob. 8CUR Ch. 7 - Prob. 9CUR Ch. 7 - Prob. 10CUR Ch. 7 - Prob. 11CUR Ch. 7 - Prob. 12CUR Ch. 7 - Solve the equation using the Zero-Product...Ch. 7 - Prob. 14CUR Ch. 7 - Prob. 15CUR Ch. 7 - Prob. 16CUR Ch. 7 - Prob. 17CUR Ch. 7 - Prob. 18CUR Ch. 7 - Prob. 19CUR Ch. 7 - Prob. 20CUR Ch. 7 - Prob. 21CUR Ch. 7 - Prob. 22CUR Ch. 7 - Prob. 23CUR Ch. 7 - Prob. 24CUR Ch. 7 - Prob. 25CUR Ch. 7 - Prob. 26CUR Ch. 7 - Prob. 27CUR Ch. 7 - Prob. 28CUR Ch. 7 - Prob. 29CUR Ch. 7 - Prob. 30CUR Ch. 7 - Prob. 1IA Ch. 7 - Prob. 2IA Ch. 7 - Prob. 3IA Ch. 7 - Prob. 4IA Ch. 7 - Prob. 5IA Ch. 7 - Prob. 6IA Ch. 7 - Prob. 7IA Ch. 7 - Prob. 8IA Ch. 7 - Prob. 9IA Ch. 7 - Prob. 10IA Ch. 7 - Prob. 11IA Ch. 7 - Prob. 12IA Ch. 7 - Prob. 13IA Ch. 7 - Prob. 14IA Ch. 7 - Prob. 15IA Ch. 7 - Prob. 16IA Ch. 7 - Prob. 17IA Ch. 7 - Prob. 18IA Ch. 7 - Prob. 19IA Ch. 7 - Prob. 20IA Ch. 7 - Prob. 21IA Ch. 7 - Prob. 22IA Ch. 7 - Prob. 23IA Ch. 7 - Prob. 24IA Ch. 7 - Prob. 25IA Ch. 7 - Prob. 26IA Ch. 7 - Prob. 27IA Ch. 7 - Prob. 28IA Ch. 7 - Prob. 29IA Ch. 7 - Prob. 30IA Ch. 7 - Prob. 31IA Ch. 7 - Prob. 32IA Ch. 7 - Prob. 33IA Ch. 7 - Prob. 34IA Ch. 7 - Prob. 35IA Ch. 7 - Solve: 7y2+y124yy2+7y+12=6y29

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The complex rational expression x − 1 − 3 x − 2 − 9 .

Solution Summary: The author explains how to simplify the complex rational expression using the definition of negative exponent.

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To simplify: The complex rational expression x−1−3x−2−9.

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Chapter 7 Solutions