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: 29

Answer

$\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}=\dfrac{a}{x+b}$

Work Step by Step

$\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}$ Evaluate the division: $\dfrac{\dfrac{ax+ab}{x^{2}-b^{2}}}{\dfrac{x+b}{x-b}}=\dfrac{ax+ab}{x^{2}-b^{2}}\div\dfrac{x+b}{x-b}=\dfrac{(ax+ab)(x-b)}{(x^{2}-b^{2})(x+b)}=...$ Take out common factor $a$ from the first parentheses in the numerator and factor the first parentheses in the denominator and then simplify: $...=\dfrac{a(x+b)(x-b)}{(x-b)(x+b)(x+b)}=\dfrac{a}{x+b}$
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