The equation 1/(x+2) + 1/(x-2) = 1 has two solutions x1 and x2. What is the product x1*x2?

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Multiple Choice

The equation 1/(x+2) + 1/(x-2) = 1 has two solutions x1 and x2. What is the product x1*x2?

Explanation:
Start with combining the fractions to get 2x/(x^2 - 4) = 1, then cross-multiply to obtain x^2 - 2x - 4 = 0. This quadratic has roots whose product is c/a, which here is -4/1 = -4. So the product x1*x2 is -4. (For reference, the roots are 1 ± sqrt(5), both valid since neither equals ±2.)

Start with combining the fractions to get 2x/(x^2 - 4) = 1, then cross-multiply to obtain x^2 - 2x - 4 = 0. This quadratic has roots whose product is c/a, which here is -4/1 = -4. So the product x1*x2 is -4. (For reference, the roots are 1 ± sqrt(5), both valid since neither equals ±2.)

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