Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 48

Answer

$\dfrac{x-6}{5x+1}+\dfrac{6}{(5x+1)^{2}}=\dfrac{x(5x-29)}{(5x+1)^{2}}$

Work Step by Step

$\dfrac{x-6}{5x+1}+\dfrac{6}{(5x+1)^{2}}$ Evaluate the sum of the two rational expressions and simplify: $\dfrac{x-6}{5x+1}+\dfrac{6}{(5x+1)^{2}}=\dfrac{(x-6)(5x+1)+6}{(5x+1)^{2}}=...$ $...=\dfrac{5x^{2}-29x-6+6}{(5x+1)^{2}}=\dfrac{5x^{2}-29x}{(5x+1)^{2}}=...$ Take out common factor of $x$ in the numerator to provide a more simplified answer: $...=\dfrac{x(5x-29)}{(5x+1)^{2}}$
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