Can't put expression in terms of y (Derivatives of Inverses Formula)

Can't put expression in terms of y (Derivatives of Inverses Formula)

Disclaimer: This is not a student posting his homework assignment.
I am an adult learning Calculus. I think this is a great forum,
Ok, you know the formula for the derivative of an inverse:
$f^{-1}(x)=\frac{1}{f'(f^{-1}(x))}$
Using this, how do you answer this one?
Find $(f^{-1})'(x)$ if $f(x)=\frac{2x-1}{x+1}$
First, using Chain rule, I determined that $f'(x) = \frac{3}{(x+1)^2}$
But, I was having trouble getting the inverse of f(x).
$y=\frac{2x-1}{x+1}$
Inverse is: $x=\frac{2y-1}{y+1}$
But, I can not put this in terms of y! What do I do?