Argh!

I'm stuck! Well, I guess that goes without saying or I wouldn't be posting.

Although I'm studying pre-calculus right now (implicit domains of composite functions), I am having trouble with an ugly fraction (well, I think so).

I can figure out the composite function with no problem, but they have simplified it to something else and I don't know how they got from this:

to this:

I am sticking with the bottom first, and trying to find a common denominator to subtract from .

I tried using as a common denominator, but I end up getting which doesn't work (unless I messed up there). I know that if you have a fraction as the denominator, you can just multiply by its reciprocal instead. So I am thinking that they figured out how to subtract from then just flipped it, which became the answer because you'd be multiplying by the numerator (1) anyway.

So how did they get from to ?