I sincerely hope this is the right forum. It's a limit problem, but the limit isn't my problem. Quick backstory if you care: I'm a 27 year old computer programmer who's trying to go through Calculus for Dummies this summer for my own education. So no, this isn't homework. I'm rapidly finding out I've forgotten a lot of basics and keep getting stuck on what I'm pretty sure is plain old algebra.
For instance, here's an example from the book:
First step is to multiply by the conjugate of the numerator and simplify
I'm good so far, but then it shows this:
(factor x out of the denominator)
The next step is just to cancel the from the numerator and denominator which I get and then do some substitution to solve the limit, but I'll save that for another post in another forum.
Anyways, I've been staring at, googling for, and whiteboard-experimenting that factoring step and I just don't follow it. It's been too long since I did any math, I guess. Can anybody explain it to me? I've subbed in some real numbers and it does work, but I don't know the rules that would let me jump from step 3 to 4.
Thanks in advance!