Multiple choice

The sum of 1/ \frac{1}{x+y}x + y and \frac{1}{x-y} is

  1. <latex>\frac{2x}{x^2-y^2}</latex>

  2. <latex>\frac{2}{2x}</latex>

  3. <latex>\frac{2y}{x^2-y^2}</latex>

  4. <latex>\frac{-2x}{x^2-y^2}</latex>
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A Correct answer
Explanation

The sum is 1/(x + y) + 1/(x - y). Find a common denominator: (x - y)/((x + y)(x - y)) + (x + y)/((x + y)(x - y)) = (x - y + x + y) / (x^2 - y^2) = 2x / (x^2 - y^2).

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