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**[SOLVED] Hyperbolic functions**

As part of a long winded "show that" question I've ended up at the point where I have [tex]xcothx[/tex] and I want to show that this is equal to [tex]cothx - \frac{1}{x}[/tex] only I have no ideas how to get there. I can't see any reason why this should be so, but I'm pretty confident that I'm correct so far (in fact I know I am!).

Obviously I could take the "magic step" when doing this kind of question (in that I could just write the final answer down, and hope that I'm close enough for this step to be intuitive) but I'd quite like to know the step to take.

Thanks in advance guys.