Explanation Given Information: The provided equation is 1 x + 1 − 9 4 x = 1 5 . Formula used: Steps to solve a rational equation: 1. Put the denominator equal to 0 and find the values which make denominator 0. These numbers cannot be the solution of the rational equation. 2. Multiply both sides of the equation by the LCM of the denominators. 3. Solve the resulting equation using addition principal, the multiplication principle and the zero products as needed. 4. Check the obtained solutions by substituting in the original equation. The distributive property for real numbers a, b and c is, a ( b + c ) = a b + a c Calculation: Consider the equation, 1 x + 1 − 9 4 x = 1 5 If x = 0 , then the denominator in 9 4 x is 0. Then, the provided equation is not defined. So, x ≠ 0 . If x = − 1 , then the denominator in 1 x + 1 is 0. Then, the provided equation is not defined. So, x ≠ − 1 . The LCM of denominators ( x + 1 ) and 4 x is 4 x ( x + 1 ) . So, multiply both sides by 4 x ( x + 1 ) , ( 1 x + 1 − 9 4 x ) ( 4 x ( x + 1 ) ) = 1 5 ( 4 x ( x + 1 ) ) Multiply the terms using the distributive property, ( 1 x + 1 ) ( 4 x ( x + 1 ) ) − ( 9 4 x ⋅ ( 4 x ( x + 1 ) ) ) = 1 5 ( 4 x ( x + 1 ) ) 4 x − 9 ( x + 1 ) = 4 x 2 + 4 x 5 4 x − 9 x − 9 = 4 x 2 + 4 x 5 − 5 x − 9 = 4 x 2 + 4 x 5 Multiply 5 to both sides using the distributive property, ( − 5 x − 9 ) 5 = 4 x 2 + 4 x 5 ⋅ 5 − 25 x − 45 = 4 x 2 + 4 x Add 25 x + 45 to both sides, 4 x 2 + 4 x + 25 x + 45 = − 25 x − 45 + 25 x + 45 4 x 2 + 29 x + 45 = 0 Factorize the equation, such that the sum of the two factors is 29 and the product is 4 ⋅ 45 = 180 . Pairs having product 180 Sum of the pairs 1, 180 181 2, 90 92 10, 18 28 9, 20 29 Since, 9 ⋅ 20 = 180 and 9 + 20 = 29 , thus the pair of factors is 9 and 29

Elementary Algebra: Concepts and Applications (10th Edition)

10th Edition

ISBN: 9780134441375

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 8, Problem 42CR

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Chapter 8, Problem 41CR

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Chapter 8 Solutions

Elementary Algebra: Concepts and Applications (10th Edition)

Ch. 8.1 - Find the square roots of 81.Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 5YT Ch. 8.1 - Prob. 6YT Ch. 8.1 - Prob. 7YT Ch. 8.1 - Prob. 8YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU

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The solution of the equation 1 x + 1 − 9 4 x = 1 5 .

Solution Summary: The author explains how to solve a rational equation using addition principal, multiplication principle, and zero products.

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Chapter 8 Solutions