Answer
$\displaystyle \frac{2x+1}{\sqrt{x}\sqrt{x+1}}$
Work Step by Step
We factor out $x^{-1/2}(x+1)^{-1/2}$:
$x^{-1/2}(x+1)^{1/2}+x^{1/2}(x+1)^{-1/2}=x^{-1/2}(x+1)^{-1/2}[(x+1)+x]=x^{-1/2}(x+1)^{-1/2}(2x+1)=\displaystyle \frac{2x+1}{\sqrt{x}\sqrt{x+1}}$
