I'm having trouble coming up with the inverse function of this:

$\displaystyle \frac{1 + e^{-x}} {1 - e^{-x}}=y=f(x) $

I might be overcomplicating how I'm going about doing this; essentially, I ended up using exponent and logarithm laws to arrive at this:

$\displaystyle \ln{(1 + e^{-y})} - \ln{(1 - e^{-y})}=\ln{x} $

Any tips? I'm thinking that I probably did overcomplicate something...