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: 51

Answer

$\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}=\dfrac{2x+21}{(x+3)^{2}}$

Work Step by Step

$\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}$ Factor the denominator of the first fraction, which is a perfect square trinomial: $\dfrac{15}{x^{2}+6x+9}+\dfrac{2}{x+3}=\dfrac{15}{(x+3)^{2}}+\dfrac{2}{x+3}=...$ Evaluate the sum of the two rational expressions and simplify: $...=\dfrac{15+2(x+3)}{(x+3)^{2}}=\dfrac{15+2x+6}{(x+3)^{2}}=\dfrac{2x+21}{(x+3)^{2}}$
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