Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Review: 62

Answer

$\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}=-\dfrac{2x+7}{2x}$

Work Step by Step

$\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}=\dfrac{\dfrac{6+4(x+2)}{x+2}}{\dfrac{8-4(x+2)}{x+2}}=\dfrac{\dfrac{6+4x+8}{x+2}}{\dfrac{8-4x-8}{x+2}}=...$ $...=\dfrac{\dfrac{4x+14}{x+2}}{\dfrac{-4x}{x+2}}=...$ Evaluate the division and simplify: $...=\dfrac{4x+14}{x+2}\div\dfrac{-4x}{x+2}=\dfrac{(4x+14)(x+2)}{-4x(x+2)}=...$ $...=\dfrac{4x+14}{-4x}=...$ Take out common factor $2$ from the numerator and simplify one more time: $...=\dfrac{2(2x+7)}{-4x}=-\dfrac{2x+7}{2x}$
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