Explanation Given: 5 2 m 2 − 5 m − 3 + 3 2 m 2 + 5 m + 2 − 1 m 2 − m − 6 Calculation: Step 1: First factorize each denominator completely to find the LCD. 2 m 2 − 5 m − 3 = ( 2 m + 1 ) ( m − 3 ) Then, 2 m 2 + 5 m + 2 = ( 2 m + 1 ) ( m + 2 ) And, m 2 − m − 6 = ( m − 3 ) ( m + 2 ) List the factors of the first denominator. 2 m 2 − 5 m − 3 = ( 2 m + 1 ) ( m − 3 ) The only factor from the other denominators that is unlisted is ( m + 2 ) . Thus, the least common denominator is ( 2 m + 1 ) ( m − 3 ) ( m + 2 ) . Step 2: Write the equivalent expressions with LCD as the denominator. Here, multiply each numerator and denominator by the extra factor that is required to form ( 2 m + 1 ) ( m − 3 ) ( m + 2 ) , and the LCD is: 5 2 m 2 − 5 m − 3 + 3 2 m 2 + 5 m + 2 − 1 m 2 − m − 6 = 5 ( 2 m + 1 ) ( m − 3 ) + 3 ( 2 m + 1 ) ( m + 2 ) − 1 ( m − 3 ) ( m + 2 ) = 5 ( 2 m + 1 ) ( m − 3 ) ⋅ ( m + 2 ) ( m + 2 ) + 3 ( 2 m + 1 ) ( m + 2 ) ⋅ ( m − 3 ) ( m − 3 ) − 1 ( m − 3 ) ( m + 2 ) ⋅ ( 2 m + 1 ) ( 2 m + 1 ) Step 3: Put the final expression over the LCD and perform the indicated operations on the numerator

Intermediate Algebra for College Students (7th Edition)

7th Edition

ISBN: 9780134178943

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 6.2, Problem 66E

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To calculate: The final result of the expression, 52m2−5m−3+32m2+5m+2−1m2−m−6.

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Chapter 6.2, Problem 65E

Chapter 6.2, Problem 67E

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Chapter 6 Solutions

Intermediate Algebra for College Students (7th Edition)

Ch. 6.1 - Check Point 1 Use the rational function in...Ch. 6.1 - Check Point 2 Find the domain of f if...Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1CVC Ch. 6.1 - Prob. 2CVC Ch. 6.1 - Prob. 3CVC

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The final result of the expression, 5 2 m 2 − 5 m − 3 + 3 2 m 2 + 5 m + 2 − 1 m 2 − m − 6 .

Solution Summary: The author explains how to calculate the final result of the expression: 6m(2m+1)

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To calculate: The final result of the expression, 52m2−5m−3+32m2+5m+2−1m2−m−6.

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Chapter 6 Solutions