Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 40

Answer

$\dfrac{x+3}{x^{2}-9}\div\dfrac{5x+15}{(x-3)^{2}}=\dfrac{x-3}{5(x+3)}$

Work Step by Step

$\dfrac{x+3}{x^{2}-9}\div\dfrac{5x+15}{(x-3)^{2}}$ Factor the denominator of the first fraction and take out common factor $5$ from the numerator of the second fraction: $\dfrac{x+3}{x^{2}-9}\div\dfrac{5x+15}{(x-3)^{2}}=\dfrac{x+3}{(x-3)(x+3)}\div\dfrac{5(x+3)}{(x-3)^{2}}=...$ Evaluate the division of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting fraction: $...=\dfrac{(x+3)(x-3)^{2}}{5(x+3)^{2}(x-3)}=\dfrac{x-3}{5(x+3)}$
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