Factor the polynomial in the numerator. We will use the polynomial fraction (x^2 - 9) / (x^2 - 2x - 15) as an example.
x^2 - 9 = (x + 3)(x - 3);
thus (x^2 - 9) / (x^2 - 2x - 15) = (x + 3)(x - 3) / (x^2 - 2x -15).
Factor the polynomial in the denominator.
(x^2 - 2x - 15) = (x - 5)(x + 3);
thus (x + 3)(x - 3) / (x^2 - 2x -15) = (x + 3)(x - 3) / [(x - 5)(x + 3)].
Cancel out common monomials or polynomials in the numerator and denominator.
(x + 3)(x - 3) / [(x - 5)(x + 3)] = (x - 3) / (x - 5)