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