Evaluate your problem and confirm that it is a polynomial. For this example, the problem will be f(x) = (x^2 - 4)/(x^2 - 5x + 6). As you can see, this is a polynomial because it contains a power of two.
Factor the top and bottom to its simplest form. In this example, for the top, x^2 factors to x * x, and -4 factors to -2 * 2. For the bottom, the factors of 6 that also add up to -5 are -2 and -3. So it comes out to: (x - 2)(x + 2)/(x - 3)(x - 2). To check, use the FOIL (First, Outside, Inside, Last) method.
Cancel out any identical components in the top and bottom. Here, you can cancel out the (x - 2), simplifying the problem to (x + 2)/(x - 3).
Graph your simplified function to see where the line crosses the x axis. These points are the solutions to the problem.