$$\frac { \sqrt { x } } { \sqrt { x + 1 } }$$
$\sqrt{\frac{x}{x+1}}$
$\frac{-\sqrt{\left(x+1\right)x^{2}}+\left(x+1\right)^{\frac{3}{2}}}{2\left(x+1\right)^{\frac{3}{2}}\sqrt{x\left(x+1\right)}}$
