x^2-5x+6/x^2-9

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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).