Explanation Given: The rational expression is. 5 x 2 3 x . Definition1 : The rational expression is, 1 a The denominator of the rational expression is, a The conjugate of the denominator is, a . Then rationalize the denominator is, 1 a × a a = a a Definition2 : Multiply the root square root number, a × a = ( a ) 2

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 1.1, Problem 66E

To determine

To evaluate: The rational expression by rationalize the denominator.

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Chapter 1.1, Problem 65E

Chapter 1.1, Problem 67E

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Describe what it means to rationalize a denominator. Use both 1/√5 and1/(5 + √5) in your explanation.

Exercises 73–80, find the difference quotientand simplify your answer.73. f(x) = x2 − 2x + 4, f(2 + h) − f(2)h , h ≠ 074. f(x) = 5x − x2, f(5 + h) − f(5)h , h ≠ 075. f(x) = x3 + 3x, f(x + h) − f(x)h , h ≠ 076. f(x) = 4x3 − 2x, f(x + h) − f(x)h , h ≠ 077. g(x) = 1x2, g(x) − g(3)x − 3 , x ≠ 378. f(t) = 1t − 2, f(t) − f(1)t − 1 , t ≠ 179. f(x) = √5x, f(x) − f(5)x − 5 , x ≠ 580. f(x) = x23 + 1, f(x) − f(8)x − 8 , x ≠ 8

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Chapter 1 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - 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Prob. 10E Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Prob. 23E Ch. 1.2 - Prob. 24E Ch. 1.2 - Prob. 25E Ch. 1.2 - Prob. 26E Ch. 1.2 - Prob. 27E Ch. 1.2 - Prob. 28E Ch. 1.2 - Prob. 29E Ch. 1.2 - Prob. 30E Ch. 1.2 - Prob. 31E Ch. 1.2 - Prob. 32E Ch. 1.2 - Prob. 33E Ch. 1.2 - Prob. 34E Ch. 1.2 - Prob. 35E Ch. 1.2 - Prob. 36E Ch. 1.2 - Prob. 37E Ch. 1.2 - Prob. 38E Ch. 1.2 - Prob. 39E Ch. 1.2 - Prob. 40E Ch. 1.2 - Prob. 41E Ch. 1.2 - Prob. 42E Ch. 1.2 - Prob. 43E Ch. 1.2 - Prob. 44E Ch. 1.2 - Prob. 45E Ch. 1.2 - Prob. 46E Ch. 1.2 - Prob. 47E Ch. 1.2 - Prob. 48E Ch. 1.2 - Prob. 49E Ch. 1.2 - Prob. 50E Ch. 1.2 - Prob. 51E Ch. 1.2 - Prob. 52E Ch. 1.2 - Prob. 53E Ch. 1.2 - Prob. 54E Ch. 1.2 - Prob. 55E Ch. 1.2 - Prob. 56E Ch. 1.2 - Prob. 57E Ch. 1.2 - Prob. 58E Ch. 1.2 - Prob. 59E Ch. 1.2 - In Exercises 4562, find the values of x that...Ch. 1.2 - Prob. 61E Ch. 1.2 - Prob. 62E Ch. 1.2 - Prob. 63E Ch. 1.2 - Prob. 64E Ch. 1.2 - Prob. 65E Ch. 1.2 - Prob. 66E Ch. 1.2 - Prob. 67E Ch. 1.2 - Prob. 68E Ch. 1.2 - Prob. 69E Ch. 1.2 - Prob. 70E Ch. 1.2 - Prob. 71E Ch. 1.2 - Prob. 72E Ch. 1.2 - Prob. 73E Ch. 1.2 - Prob. 74E Ch. 1.2 - Prob. 75E Ch. 1.2 - Prob. 76E Ch. 1.2 - Prob. 77E Ch. 1.2 - Prob. 78E Ch. 1.2 - Prob. 79E Ch. 1.2 - Prob. 80E Ch. 1.2 - Prob. 81E Ch. 1.2 - Prob. 82E Ch. 1.2 - Prob. 83E Ch. 1.2 - Prob. 84E Ch. 1.2 - Prob. 85E Ch. 1.2 - Prob. 86E Ch. 1.2 - Prob. 87E Ch. 1.2 - Prob. 88E Ch. 1.2 - Prob. 89E Ch. 1.2 - Prob. 90E Ch. 1.2 - Prob. 91E Ch. 1.2 - Prob. 92E Ch. 1.2 - Prob. 93E Ch. 1.2 - Prob. 94E Ch. 1.2 - Prob. 95E Ch. 1.2 - Prob. 96E Ch. 1.2 - Prob. 97E Ch. 1.2 - Prob. 98E Ch. 1.2 - Prob. 99E Ch. 1.2 - Prob. 100E Ch. 1.2 - Prob. 101E Ch. 1.2 - Prob. 102E Ch. 1.3 - Prob. 1CQ Ch. 1.3 - Prob. 2CQ Ch. 1.3 - Prob. 1E Ch. 1.3 - Prob. 2E Ch. 1.3 - Prob. 3E Ch. 1.3 - Prob. 4E Ch. 1.3 - Prob. 5E Ch. 1.3 - Prob. 6E Ch. 1.3 - Prob. 7E Ch. 1.3 - Prob. 8E Ch. 1.3 - Prob. 9E Ch. 1.3 - Prob. 10E Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - Prob. 14E Ch. 1.3 - Prob. 15E Ch. 1.3 - Prob. 16E Ch. 1.3 - Prob. 17E Ch. 1.3 - Prob. 18E Ch. 1.3 - Prob. 19E Ch. 1.3 - Prob. 20E Ch. 1.3 - Prob. 21E Ch. 1.3 - Prob. 22E Ch. 1.3 - Prob. 23E Ch. 1.3 - Prob. 24E Ch. 1.3 - Find the coordinates of the points that are 10...Ch. 1.3 - Prob. 26E Ch. 1.3 - Prob. 27E Ch. 1.3 - Prob. 28E Ch. 1.3 - Prob. 29E Ch. 1.3 - Prob. 30E Ch. 1.3 - Prob. 31E Ch. 1.3 - Prob. 32E Ch. 1.3 - Prob. 33E Ch. 1.3 - Prob. 34E Ch. 1.3 - Prob. 35E Ch. 1.3 - Prob. 36E Ch. 1.3 - WILL YOU INCUR A DELIVERY CHARGE? A furniture...Ch. 1.3 - Prob. 38E Ch. 1.3 - MINIMIZING SHIPPING COSTS FOR A FLEET OF AUTOS...Ch. 1.3 - Prob. 40E Ch. 1.3 - Prob. 41E Ch. 1.3 - Prob. 42E Ch. 1.3 - Prob. 43E Ch. 1.3 - WATCHING A ROCKET LAUNCH At a distance of 4000 ft...Ch. 1.3 - Prob. 45E Ch. 1.3 - A SCAVENGER HUNT A tree is located 20 yd to the...Ch. 1.3 - Prob. 47E Ch. 1.3 - Prob. 48E Ch. 1.3 - Prob. 49E Ch. 1.3 - Prob. 50E Ch. 1.3 - Prob. 51E Ch. 1.3 - Prob. 52E Ch. 1.4 - Prob. 1CQ Ch. 1.4 - Prob. 2CQ Ch. 1.4 - Prob. 3CQ Ch. 1.4 - Prob. 4CQ Ch. 1.4 - Prob. 1E Ch. 1.4 - Prob. 2E Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.4 - Prob. 8E Ch. 1.4 - Prob. 9E Ch. 1.4 - Prob. 10E Ch. 1.4 - In Exercises 11-16, find the slope of the line...Ch. 1.4 - Prob. 12E Ch. 1.4 - In Exercises 11-16, find the slope of the line...Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 36E Ch. 1.4 - Prob. 37E Ch. 1.4 - Prob. 38E Ch. 1.4 - Prob. 39E Ch. 1.4 - Prob. 40E Ch. 1.4 - Prob. 41E Ch. 1.4 - Prob. 42E Ch. 1.4 - Prob. 43E Ch. 1.4 - Prob. 44E Ch. 1.4 - Prob. 45E Ch. 1.4 - Find an equation of the line that passes through...Ch. 1.4 - Prob. 47E Ch. 1.4 - Prob. 48E Ch. 1.4 - Prob. 49E Ch. 1.4 - Prob. 50E Ch. 1.4 - Prob. 51E Ch. 1.4 - Prob. 52E Ch. 1.4 - Prob. 53E Ch. 1.4 - Prob. 54E Ch. 1.4 - Prob. 55E Ch. 1.4 - Prob. 56E Ch. 1.4 - Prob. 57E Ch. 1.4 - Prob. 58E Ch. 1.4 - Prob. 59E Ch. 1.4 - Prob. 60E Ch. 1.4 - Prob. 61E Ch. 1.4 - Prob. 62E Ch. 1.4 - Prob. 63E Ch. 1.4 - Prob. 64E Ch. 1.4 - Prob. 65E Ch. 1.4 - Prob. 66E Ch. 1.4 - Prob. 67E Ch. 1.4 - Prob. 68E Ch. 1.4 - Prob. 69E Ch. 1.4 - Prob. 70E Ch. 1.4 - Prob. 71E Ch. 1.4 - Prob. 72E Ch. 1.4 - Prob. 73E Ch. 1.4 - Prob. 74E Ch. 1.4 - Prob. 75E Ch. 1.4 - Prob. 76E Ch. 1.4 - Prob. 77E Ch. 1.4 - Prob. 78E Ch. 1.4 - SPENDING ON EQUIPMENT AND SOFTWARE As the United...Ch. 1.4 - SALES GROWTH Metro Department Stores annual sales...Ch. 1.4 - Prob. 81E Ch. 1.4 - Prob. 82E Ch. 1.4 - Prob. 83E Ch. 1.4 - Prob. 84E Ch. 1.4 - Prob. 85E Ch. 1.4 - Prob. 86E Ch. 1.4 - Prob. 87E Ch. 1.4 - Prob. 88E Ch. 1.4 - Prob. 89E Ch. 1.4 - Prob. 90E Ch. 1 - Prob. 1CRQ Ch. 1 - Prob. 2CRQ Ch. 1 - Prob. 3CRQ Ch. 1 - Prob. 4CRQ Ch. 1 - Prob. 5CRQ Ch. 1 - Prob. 6CRQ Ch. 1 - Prob. 7CRQ Ch. 1 - Prob. 8CRQ Ch. 1 - Prob. 1RE Ch. 1 - Prob. 2RE Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - In Exercises 2932, find the value(s) of x that...Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - Prob. 48RE Ch. 1 - Prob. 49RE Ch. 1 - Prob. 50RE Ch. 1 - Prob. 51RE Ch. 1 - Prob. 52RE Ch. 1 - Prob. 53RE Ch. 1 - Prob. 54RE Ch. 1 - Prob. 55RE Ch. 1 - Prob. 56RE Ch. 1 - Prob. 57RE Ch. 1 - Prob. 58RE Ch. 1 - Prob. 59RE Ch. 1 - Prob. 60RE Ch. 1 - Prob. 61RE Ch. 1 - Prob. 62RE Ch. 1 - Prob. 1BM Ch. 1 - Prob. 2BM Ch. 1 - Prob. 3BM Ch. 1 - Prob. 4BM Ch. 1 - Prob. 5BM Ch. 1 - Prob. 6BM Ch. 1 - Prob. 7BM Ch. 1 - Prob. 8BM Ch. 1 - Prob. 9BM Ch. 1 - Prob. 10BM

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The rational expression by rationalize the denominator.

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Chapter 1 Solutions