Mathematica seems to have trouble with expressions like
Oddly, it doesn't have trouble with
which will happily simplify to $1$ even without invoking
Simplify. I know that usually
FullSimplify not doing what you expect is because of unconscious assumptions you're not telling Mathematica about, but I'm at a loss as for what value of $x$ I could be talking about where the above two expressions wouldn't be equal...
At any rate, is there any way to force
FullSimplify to give the expected result (i.e. $1$) in the first of the above cases?