Answer
$\frac{x+2}{(1+x)^{3/2}}$
Work Step by Step
We factor out $(1+x)^{-1/2}$, remembering that $(1+x)=(1+x)^{-1/2}*(1+x)^{1/2}$:
$\displaystyle \frac{2(1+x)^{1/2}-x(1+x)^{-1/2}}{1+x}=\frac{(1+x)^{-1/2}[2(1+x)-x]}{1+x}=\frac{x+2}{(1+x)^{3/2}}$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises - Page 52: 81
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