What is one value that makes the fraction (4x – 8) ⁄ (x 2 + x – 42) undefined?

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Accepted Answer

A fraction is undefined when its denominator is equal to 0. Factor the quadratic in the denominator and set each factor equal to 0 to find the values that make the fraction undefined. 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; –6 and 7 multiply to –42 and add to 1. Therefore, the factors of x 2 + x – 42 are (x – 6) and (x + 7). Set each factor equal to 0 and solve for x: x – 6 = 0, x = 6, and x + 7 = 0, x = –7. When x equals 6 or –7, the fraction is undefined.

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