What values make the fraction (x 2 + 8x + 7) ⁄ (x 2 – 8x + 7) 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; –1 and –7 multiply to 7 and add to –8. Therefore, the factors of x 2 – 8x + 7 are (x – 1) and (x – 7). Set each factor equal to 0 and solve for x: x – 1 = 0, x = 1, and x – 7 = 0, x = 7. When x equals 1 or 7, the fraction is undefined.

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