Question

$$y=\frac{\sqrt{x}}{x-2}$$

Solve for x

$\left\{\begin{matrix}x=\frac{\left(\frac{\sqrt{8y^{2}+1}-1}{y}\right)^{2}}{4}\text{, }&y<0\\x=\frac{\left(\frac{\sqrt{8y^{2}+1}+1}{y}\right)^{2}}{4}\text{, }&y>0\\x=0\text{, }&y=0\end{matrix}\right.$

Solve for y

$y=\frac{\sqrt{x}}{x-2}$
$x\geq 0\text{ and }x\neq 2$