Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 52

Answer

$\dfrac{2}{x^{2}+4x+4}+\dfrac{1}{x+2}=\dfrac{x+4}{(x+2)^{2}}$

Work Step by Step

$\dfrac{2}{x^{2}+4x+4}+\dfrac{1}{x+2}$ Factor the denominator of the first fraction, which is a perfect square trinomial: $\dfrac{2}{x^{2}+4x+4}+\dfrac{1}{x+2}=\dfrac{2}{(x+2)^{2}}+\dfrac{1}{x+2}=...$ Evaluate the sum of the two rational expressions and then simplify: $...=\dfrac{2+(x+2)}{(x+2)^{2}}=\dfrac{x+4}{(x+2)^{2}}$
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