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})
Correct Answer: Option B
Explanation
(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})