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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.

$\frac{y}{x^2 - y^2}$

View answer & explanation

Correct answer is B

$\frac{x}{x + y}$ + $\frac{y}{x - y}$ - $\frac{x^2}{x^2 - y^2}$

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

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

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

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

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

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