The fraction (x + 9) ⁄ (x 2 – 81) is equivalent to

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Factor the denominator. To find the factors of a quadratic, begin by finding two numbers whose product is equal to the constant of the quadratic. Of those numbers, find the pair that adds to the coefficient of the x term of the quadratic. This quadratic has no x term—the sum of the products of the outside and inside terms of the factors is 0; –9 and 9 multiply to –81 and add to 0. Therefore, the factors of x 2 – 81 are (x – 9) and (x + 9). Cancel the (x + 9) terms from the numerator and denominator, leaving 1 in the numerator and (x – 9) in the denominator.

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