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: 37

Answer

$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}=\dfrac{3x+4y}{2(x+2y)}$

Work Step by Step

$\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}$ Factor the denominator of the first fraction, which is a perfect square trinomial: $\dfrac{3x+4y}{x^{2}+4xy+4y^{2}}\cdot\dfrac{x+2y}{2}=\dfrac{3x+4y}{(x+2y)^{2}}\cdot\dfrac{x+2y}{2}=...$ Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{(3x+4y)(x+2y)}{2(x+2y)^{2}}=\dfrac{3x+4y}{2(x+2y)}$
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