Simplify: $${e^{-2x}-1\over e^x+1}$$

The question I am trying to answer is actually concerned with finding the derivative of this expression. However, simplifying this expression before differentiating makes that task trivial. The problem is that I cannot find a way to simplify this expression into the equivalent expression, ${1-e^x\over e^{2x}}$, or $-e^{-2x}(e^x-1)$. 

I have a feeling I will feel quite stupid when I see what I am missing but any help would be greatly appreciated.