What is the inverse function of sqrt(x)/sqrt(x+1)

Question

I can't figure out how to find the inverse of $\frac{\sqrt{x}}{\sqrt{x+1}}$

Here's my process:

$y = \frac{\sqrt{x}}{\sqrt{x+1}}\\ y\sqrt{x+1} = \sqrt{x}\\y²(x+1)=x\\xy²+y²=x\\xy²-x=-y²\\x(y²-1)=-y²\\x=\frac{-y²}{y²-1}$

But this is incorrect for some reason, I just don't see anything wrong with it.

Could you help me get past this?

Thanks.