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