Explanation Given Information: The provided equation is, x 2 x 2 − 4 = x x + 2 − 2 x 2 − x Formula used: Use the following steps to solve the equation of fractions: Step 1: Find the least common multiple or LCM by factorization of each term in the denominator completely. Step 2: Multiply the terms on both sides of the equation by the LCM of all the denominators. Step 3: Simplify the obtained equation. Algebraic identity: a 2 − b 2 = ( a + b ) ( a − b ) Zero product rule: An equation a b = 0 is true if and only if a = 0 or b = 0 , or both. A product is zero if and only if at least one factor is zero. Calculation: Consider the provided equation of fractions, x 2 x 2 − 4 = x x + 2 − 2 x 2 − x Rewrite the above equation as below: x 2 x 2 − 4 = x x + 2 − ( − 2 x x − 2 ) x 2 x 2 − 4 = x x + 2 + 2 x x − 2 The terms in the denominator are ( x − 2 ) , ( x + 2 ) and ( x 2 − 4 ) . Therefore, The factor of ( x − 2 ) is ( x − 2 ) . The factor of ( x + 2 ) is ( x + 2 ) . And, the factor of ( x 2 − 4 ) is, ( x 2 − 4 ) = ( x + 2 ) ( x − 2 ) The term ( x − 2 ) and ( x + 2 ) appears only one time. Therefore, LCM is, ( x + 2 ) ( x − 2 ) Multiply by least common multiple ( x + 2 ) ( x − 2 ) on both sides and solve as below: x 2 x 2 − 4 = x x + 2 + 2 x x − 2 ( x + 2 ) ( x − 2 ) × ( x 2 x 2 − 4 ) = ( x + 2 ) ( x − 2 ) × ( x x + 2 + 2 x x − 2 ) Open the bracket and use a 2 − b 2 = ( a + b ) ( a − b ) , multiply by each term and simplify further: ( x + 2 ) ( x − 2 ) × ( x 2 x 2 − 4 ) =

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 12.7, Problem 46ES

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To calculate: The solution for the equation x2x2−4=xx+2−2x2−x.

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Chapter 12.7, Problem 45ES

Chapter 12.7, Problem 47ES

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The solution for the equation x 2 x 2 − 4 = x x + 2 − 2 x 2 − x .

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To calculate: The solution for the equation x2x2−4=xx+2−2x2−x.

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