Problem: $\displaystyle \frac{x - 8}{x^2 - 4} + \frac{3}{x^2-2x}$

Answer: $\displaystyle \frac{x-3}{x(x+2)}, x\not=2 $

What I ended up with: $\displaystyle \frac{x^2-5x+6}{x(x^2 - 4)} $

Any help on how to do problems like this would be great as well. I feel like I was doing everything correctly, but now that I'm at the end I don't see any way to make my answer look like the one in the book.