Answer
$\dfrac{2(1+x)^{1/2}-x(1+x)^{-1/2}}{x+1}=\dfrac{x+2}{\sqrt{(x+1)^{3}}}$
Work Step by Step
$\dfrac{2(1+x)^{1/2}-x(1+x)^{-1/2}}{x+1}$
Take out common factor $(1+x)^{-1/2}$ from the numerator and simplify:
$\dfrac{2(1+x)^{1/2}-x(1+x)^{-1/2}}{x+1}=\dfrac{(1+x)^{-1/2}[2(1+x)-x]}{x+1}=...$
$...=\dfrac{(1+x)^{-1/2}(2+2x-x)}{x+1}=\dfrac{(1+x)^{-1/2}(x+2)}{(x+1)}=...$
$...=\dfrac{x+2}{(x+1)(x+1)^{1/2}}=\dfrac{x+2}{(x+1)^{3/2}}=\dfrac{x+2}{\sqrt{(x+1)^{3}}}$
