Explanation Given information: The provided equation is: 2 − a − 2 a + 3 = a 2 − 4 a + 3 Formula used: Find the least common multiple or LCM by factorization of each term in the denominator completely, use each factor “the greatest number of times it occurred” and multiply it. Use the formula as below: a 2 − b 2 = ( a + b ) ( a − b ) Calculation: The equation to solve as below: 2 − a − 2 a + 3 = a 2 − 4 a + 3 The terms lies in the denominator is a + 3 . Therefore, The factors of a + 3 is a + 3 . The term a + 3 appears only one time. Therefore, LCM is, a + 3 . Multiply least common multiple on both sides and solve as below: 2 − a − 2 a + 3 = a 2 − 4 a + 3 ( a + 3 ) × ( 2 − a − 2 a + 3 ) = ( a + 3 ) × ( a 2 − 4 a + 3 ) Open the bracket, multiply by each term and simplify further: ( a + 3 ) × 2 − ( a + 3 ) × a − 2 a + 3 = ( a + 3 ) × ( a 2 − 4 a + 3 ) 2 ( a + 3 ) − ( a − 2 ) = a 2 − 4 2 a + 6 − a + 2 = a 2 − 4 a + 8 = a 2 − 4 Further solve and find the value as below: a + 8 − a − 8 = a 2 − 4 − a − 8 a 2 − a − 12 = 0 ( a − 4 ) ( a + 3 ) = 0 a = 4 , − 3 Thus, the solution of “ a ” is 4 and − 3

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Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 12.7, Problem 43ES

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To calculate: The solution for the provided equation 2−a−2a+3=a2−4a+3.

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Chapter 12.7, Problem 42ES

Chapter 12.7, Problem 44ES

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Chapter 12 Solutions

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Ch. 12.1 - Objective 11.3a: Factor trinomials of the type...Ch. 12.1 - Prob. 2SR Ch. 12.1 - Prob. 1DE Ch. 12.1 - Prob. 2DE Ch. 12.1 - Prob. 3DE Ch. 12.1 - Prob. 4DE Ch. 12.1 - Prob. 5DE Ch. 12.1 - Prob. 6DE Ch. 12.1 - Prob. 7DE Ch. 12.1 - Prob. 8DE

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The solution for the provided equation 2 − a − 2 a + 3 = a 2 − 4 a + 3 .

Solution Summary: The author explains how to calculate the solution for the provided equation 2-a-2 a+3 by factorization of each term in the denominator completely.

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To calculate: The solution for the provided equation 2−a−2a+3=a2−4a+3.

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