Solve y=x-2/(1-x)^1/2

$$y = \frac { x - 2 } { ( 1 - x ) ^ { 1 / 2 } }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1-\frac{4}{y^{2}}}y^{2}}{2}-\frac{y^{2}}{2}+2\text{, }&arg(\frac{-\sqrt{1-\frac{4}{y^{2}}}y+y}{2})\geq \pi \text{ and }y\neq 0\\x=-\frac{\sqrt{1-\frac{4}{y^{2}}}y^{2}}{2}-\frac{y^{2}}{2}+2\text{, }&arg(\frac{\sqrt{1-\frac{4}{y^{2}}}y+y}{2})\geq \pi \text{ and }y\neq 0\\x=2\text{, }&y=0\end{matrix}\right.$$

Solve for y (complex solution)

$$y=-\left(1-x\right)^{-\frac{1}{2}}\left(2-x\right)$$

$$x\neq 1$$

Solve for x

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

Solve for y

$$y=-\frac{2-x}{\sqrt{1-x}}$$

$$x<1$$