Explanation Given information: The provided equation is: t + 5 t − 2 = t − 2 t + 4 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. Calculation: The equation to solve as below: t + 5 t − 2 = t − 2 t + 4 The terms lies in the denominator is t − 2 and t + 4 . Therefore, The factors of t − 2 is t − 2 . The factors of t + 4 is t + 4 . The term t − 2 and t + 4 appears only one time. Therefore, LCM is, ( t − 2 ) ⋅ ( t + 4 ) = ( t − 2 ) ( t + 4 ) Therefore, the least common multiple of the denominators is ( t − 2 ) ( t + 4 ) . Multiply by least common multiple on both sides and solve as below: t + 5 t − 2 = t − 2 t + 4 ( t + 4 ) ( t − 2 ) × ( t + 5 t − 2 ) = ( t + 4 ) ( t − 2 ) × ( t − 2 t + 4 ) ( t + 4 ) ( t + 5 ) = ( t − 2 ) ( t − 2 ) Multiply and simplify further: t ( t + 5 ) + 4 ( t + 5 ) = t ( t − 2 ) − 2 ( t − 2 ) t 2 + 5 t + 4 t + 20 = t 2 − 2 t

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ISBN: 9781323235911

Author: BITTINGER

Publisher: Pearson Custom Publishing

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Chapter 12.7, Problem 36ES

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To calculate: The solution for the provided equation t+5t−2=t−2t+4.

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Chapter 12.7, Problem 35ES

Chapter 12.7, Problem 37ES

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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 t + 5 t − 2 = t − 2 t + 4 .

Solution Summary: The author explains the formula used to calculate the least common multiple or LCM by factorization of each term in the denominator completely, using each factor "the greatest number of times it occurred".

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To calculate: The solution for the provided equation t+5t−2=t−2t+4.

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