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Simplify $\frac{x^2 - y^2}{2x^2 + xy - y^2}$ ...

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

A.

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

B.

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

C.

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

D.

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

View answer & explanation

Correct answer is C

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

$2x^{2} + xy - y^{2} = 2x^{2} - xy + 2xy - y^{2}$

= $x(2x - y) + y(2x - y)$

= $(x + y)(2x - y)$

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

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

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