Polynomial fractions usually can be simplified by doing necessary transformation and factoring so that common factors in the numerator and denominator can be canceled out. For example, (x^2 - 9) / (x^2 - 2x -15) can be simplified into (x - 3) / (x - 5) by factoring both the numerator and the denominator, and canceling the factor (x + 3). The complexity of simplifying polynomial fractions lies in the process of figuring out how to factor the numerator and the denominator.
Instructions
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1
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).
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2
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)].
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3
Cancel out common monomials or polynomials in the numerator and denominator.
(x + 3)(x - 3) / [(x - 5)(x + 3)] = (x - 3) / (x - 5)