I've given this a try but I don't think I'm doing it right. If someone could explain what the best way to go about this that would be great. Thanks in advance.

Question (simplify this fraction):

(x/x-2)-(10/(x+3)(x-2))

I tried to get a common denominator and expand out of the brackets but I have a feeling I'm going about this wrong.

I did:

(x^3+x^2-6x+10x-20)/(x^3+x^2-6x-2x^2-2x+12)

(x^3+x^2+4x-20)/(x^3-x^2-8x+12)

(4x-20)/(-8x+12)

However I'm pretty sure I'm doing it wrong.

Thanks!