Simplify the complex fraction: [(1/x) - (1/y)] / [(1/x^2) - (1/y^2)].

Answer and explanation

Correct answer: D. x*y / (x + y)

  1. Step 1: Find common denominators in numerator: (y - x) / (x*y).
  2. Step 2: Factor denominator: (1/x - 1/y)(1/x + 1/y) = [(y - x)/(xy)] [(x + y)/(x*y)].
  3. Step 3: Divide numerator by denominator: [(y - x)/(xy)] / {[(y - x)/(xy)] [(x + y)/(xy)]}.
  4. Step 4: Cancel common factor: 1 / [(x + y)/(xy)] = xy / (x + y).
Answer
x*y / (x + y).
Why not the others: '(x + y) / (xy)' inverts the quotient; 'xy / (y - x)' fails to recognize difference of squares; '1 / (x + y)' drops the product x*y.

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