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

Can this be simplified as -x^2/(2x-3)? If so, how?

yes, as long as x≠1

(1-x) = -(x-1), so you have

-x^2(x-1)
-------------
(2x-3)(x-1)

and the x-1 factors cancel.