Simplify \(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)

  • A \(\frac{x}{x^2 - y^2}\)
  • B \(\frac{y^2}{x^2 - y^2}\)
  • C \(\frac{x^2}{x^2 - y^2}\)
  • D \(\frac{y}{x^2 - y^2}\)

The correct answer is B. \(\frac{y^2}{x^2 - y^2}\)

\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\) \(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{(x + y)(x - y}\) = \(\frac{x(x - y) + y(x + y) - x^2}{(x + y)(x - y}\) = \(\frac{x^2 + xy + xy + y^2 - x^2}{(x + y)(x - y}\) = \(\frac{y^2}{(x + y)(x - y)}\) = \(\frac{y^2}{(x^2 - y^2)}\)

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