Question

u^2+3u/u^2+2u-3 X u^3-u/u^2-u-2

Answer 1

What a mess

I am sure you meant:
(u^2+3u)/(u^2+2u-3) (u^3-u)/(u^2-u-2)

= u(u+3)/( (u+3)(u-1) ) (u(u-1)(u+1))/( (u-2)(u+1) )
= u^2/(u-2) , u ≠ -3, -1, 1, 2