Simplyfy, ((x-2)(x^2+5x+6)-(2x^2+10x+12))/(x^2+x-2)

The key to this is to not expand everything out and try work it out through that process. The easiest way is to notice that (x^2+5x+6) = (x+2), (2x^2+10x+12)=2(x+3)(x+2) and (x^2+x-2)= (x+2)(x-1).From this we can then notice there is a factor of (x+2) in every term so we "get rid" of that. Which makes it a lot easier to expand out the brackets to get (x^2-x-3)/(x-1)