If x + 5 ⁄ 4 = 6x – 6 ⁄ x + 4 , what is one possible value of x?

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Accepted Answer

Cross multiply: (x + 5)(x + 4) = (4)(6x – 6), x 2 + 9x + 20 = 24x – 24. Combine like terms on one side of the equation and set the expression equal to 0; x 2 + 9x + 20 = 24x – 24, x 2 – 15x + 44 = 0. Factor the quadratic and set each factor equal to 0 to find the solutions for x. 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; –4 and –11 multiply to 44 and add to –15. Therefore, the factors of x 2 – 15x + 44 are (x – 4) and (x – 11). Set each factor equal to 0 and solve for x: x – 4 = 0, x = 4, and x – 11 = 0, x = 11.

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