What values make the fraction (x 2 – 36) ⁄ (2x 2 – 25x + 72) undefined?

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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. Since the first term of the quadratic is 2x 2 , the factors of the quadratic will be (2x + c)(x + d), where c and d are constants that multiply to 72 and add to –25 after either c or d is multiplied by 2. –8 and –9 multiply to 72, and 2(–8) + (–9) = –25. Therefore, the factors of 2x 2 – 25x + 72 are (2x – 9) and (x – 8). Set each factor equal to 0 and solve for x: 2x – 9 = 0, 2x = 9, x = 9 ⁄ 2 , and x – 8 = 0, x = 8. When x equals 9 ⁄ 2 or 8, the fraction is undefined.

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