Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set: 53

Answer

$\dfrac{x^{2}+5x}{x^{2}-25}\cdot\dfrac{3x-15}{x^{2}}=\dfrac{3}{x}$

Work Step by Step

$\dfrac{x^{2}+5x}{x^{2}-25}\cdot\dfrac{3x-15}{x^{2}}$ Factor both rational expressions completely: $\dfrac{x^{2}+5x}{x^{2}-25}\cdot\dfrac{3x-15}{x^{2}}=\dfrac{x(x+5)}{(x+5)(x-5)}\cdot\dfrac{3(x-5)}{x^{2}}=...$ Evaluate the product and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{3x(x+5)(x-5)}{x^{2}(x+5)(x-5)}=\dfrac{3}{x}$
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