Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 429: 100

Answer

False

Work Step by Step

In the given statement, common terms have been cancelled in addition, which is wrong. The correct solution is: $$\begin{align*} \dfrac{1}{x+3}+\dfrac{x+3}{2}&=\dfrac{2}{2(x+3)}+\dfrac{(x+3)^2}{2(x+3)}\\ &=\dfrac{2+(x+3)^2}{2(x+3)}\\ &=\dfrac{2+x^2+6x+9}{2(x+3)}\\ &=\dfrac{x^2+6x+11}{2(x+3)}. \end{align*}$$ So the given statement is FALSE. A true statement is: $$\dfrac{1}{x+3}+\dfrac{3x+7}{2(x+3)}=\dfrac{3}{2}.$$
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