This one's driving me up the wall. It's not for homework, but I'm re-entering the math world after a liberal arts stint and am trying to be a perfectionist about it.

The expression:

(the -1/2 and 1/2 following the raised left parentheses are both supposed to be fractional exponents)

The book's answer:

I'd just scan and post an image of the pages I've devoted solely to this problem if they were at all legible. Instead, I'll summarize my approaches to this problem:

I've tried putting (x-1)^1/2 in the denominator, then factoring everything out. I've tried putting that in the denominator, then adding like bases and factoring it out. I've tried just adding like bases to begin with, which totally prevented me from putting (x-1)^1/2 in the denominator. I've also tried squaring the whole problem to get rid of any (1/2) exponent and factoring it out. I even bought the Bagatrix "Algebra Solved!" software and had it try to simplify the problem, yet its answer doesn't match my books; its process matches my factoring process. I've double checked whether I've copied the initial problem correctly and I have.

There must be something I'm missing, but I have no idea what. Please help!

Thanks in advance.

P.S. Sorry about the formatting. Just blame my n00bhood.