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