I'm meant to put coth(x) in terms of e^x and e^-x. I keep end up getting the wrong answer and I have no idea how to do it.

My final answer is $\displaystyle \frac{e^{2x} + 2 + e^{-2x}}{e^{2x} - e^{-2x}}$

Those of you that can actually do this probably thinking 'How on earth did he come to that?'