Solve $y = \frac{x}{|1 - x|}$ for $x$

Question

I have the following equation $y=x|1-x|^{-1}$ And I need to rearrange this for x

I've tried many things, however I can't work out the answer

Current working:

$\frac{y}{x}=1/|1-x|$

$\frac{x}{y}=|1-x|$

$\frac{x}{y}=√((1-x)^2)$

Answer 1

Hint: assuming you're only interested in real solutions, $|1-x|$ is either $1-x$ or $-(1-x)$.

Answer 2

Hint:

If you drop the absolute value for a while, you can write

$$y=\pm\frac x{1-x}$$

which is solved by

$$x=1-\frac1{\pm y+1}.$$

Remains tp discuss in terms of the sign of $1-x$ or $\pm y+1$.