Factor the top and bottom first.
x^2 - 5x + 6 becomes (x - 3) (x -2).
x^2 - 9 becomes (x - 3) (x + 3).
We now have this fraction: (x - 3) (x -2)/(x - 3) (x + 3).
Cancel out common factors. We can cancel out factors that are the same on the top and bottom.
In this case, we cancel out (x - 3) from the top and bottom.
Final answer: (x - 2)/(x + 3).