College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding: 87

Answer

$\displaystyle \frac{3x+2}{(1+x)^{1/2}}$

Work Step by Step

We simplify: $\displaystyle \frac{x}{(1+x)^{1/2}}+2(1+x)^{1/2}=\frac{x}{(1+x)^{1/2}}+2(1+x)^{1/2}\frac{(1+x)^{1/2}}{(1+x)^{1/2}}=\frac{x+2(1+x)^{1/2}(1+x)^{1/2}}{(1+x)^{1/2}}=\frac{x+2(1+x)}{(1+x)^{1/2}}=\frac{x+2+2x}{(1+x)^{1/2}}=\frac{3x+2}{(1+x)^{1/2}}$
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