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:





2 Answers 2


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



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 $\pm y+1$.


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