[SOLVED] subtracting fractions

this should probably be fairly easy, but my answer ended up being slightly different than what the answer should be. I'm hoping someone can be so kind as to point out my mistake.

I started by factoring the denominators to

then I multiplied the stuff out to

I then factored out the (x-2) in the numerator to

then cancelled the (x-2) out, leaving

next I distributed the numerator to

then finally simplified to

unfortunately, the answer is apparently

close, but close doesn't count in math. Can someone please point out my mistake?