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Simplify \(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac...

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.

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

Correct answer is B

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

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

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

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

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

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