Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set - Page 549: 36



Work Step by Step

$\dfrac{\dfrac{25}{x+5}+5}{\dfrac{3}{x+5}-5}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{25}{x+5}+5}{\dfrac{3}{x+5}-5}=\dfrac{\dfrac{25+5(x+5)}{x+5}}{\dfrac{3-5(x+5)}{x+5}}=\dfrac{\dfrac{25+5x+25}{x+5}}{\dfrac{3-5x-25}{x+5}}=...$ $...=\dfrac{\dfrac{5x+50}{x+5}}{\dfrac{-5x-22}{x+5}}=...$ Evaluate the division: $...=\dfrac{5x+50}{x+5}\div\dfrac{-5x-22}{x+5}=\dfrac{(5x+50)(x+5)}{(x+5)(-5x-22)}=...$ Take out common factor $5$ from the first parentheses in the numerator and simplify if possible: $...=\dfrac{5(x+10)(x+5)}{(x+5)(-5x-22)}=\dfrac{5(x+10)}{-5x-22}=-\dfrac{5(x+10)}{5x+22}$
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