Help with a pre-calculus math problem

Factor the following completely:
(x^2-x)(1-x^2)^(-3/2) + (1-x^2)^(-1/2)(2x-1)

Any help would be great. Thanks in advance.

(x^2-x)(1-x^2)^(-3/2) + (1-x^2)^(-1/2)(2x-1)....factor out the smallest power of the common factor.

(1-x^2)^(-3/2) [ x^2-x+ (1-x^2)(2x-1)]

= (1-x^2)^(-3/2) [ x^2 -x + 2x-1 -2x^3+x^2]

= (1-x^2)^(-3/2) [ -2x^3+2x^2 +x -1]

= (1-x^2)^(-3/2) [ -2x^2 ( x-1)+(x-1)]

= (x-1)(1-x^2)^(-3/2) (1-2x^2).... This is pretty good, but you can still rearrange a little.
Take (x-1)= -(1-x) and 1-2x^2= -(2x^2-1)
Then factor 1-x^2= (1-x)(1+x)

= (1-x) (2x^2-1)(1-x)^(-3/2)(1+x)^(-3/2)

= (2x^2-1)/[ (1-x)^ (1/2) * (1+x)^(3/2)]

Hoping this helps!