I see how Educated's tip solved the problem, I'm just not sure how I'd have figured that out on my own. It seems arbitrary to multiply everything by until you actually do it.
So if I were to receive this problem on a test, how would I know to do that? Identities are very frustrating for me. It often seems like trying random things until something works.
Just a note: in LaTeX when you use \frac it gives you smaller fractions eg. . This gets really hard to read if you have fractions on fractions. Use \dfrac to give bigger fractions eg.
This gives you the answer straight away.
Doing this is more suggestive (I would have thought) than the approach you ended up taking (which pretty much pulls a rabbit out of the hat). You do it as the next step from what you had way back in post #3.