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if p=x/x+y q=y/x+y then the value of 1/p-q - 2q/p^2-q^2

Dear student

We have, p = \frac{x}{x + y} and q = \frac{y}{x + y} So, \frac{1}{p - q} - \frac{2 q}{p^{2} - q^{2}} = \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} - \frac{2 (\frac{y}{x + y})}{{(\frac{x}{x + y})}^{2} - {(\frac{y}{x + y})}^{2}} = \frac{1}{\frac{x - y}{x + y}} - \frac{\frac{2 y}{x + y}}{\frac{x^{2} - y^{2}}{x + y}} = \frac{x + y}{x - y} - [\frac{2 y}{x + y} \times \frac{x + y}{(x - y) (x + y)}] = \frac{x + y}{x - y} - [\frac{2 y}{(x + y) (x - y)}] = \frac{{(x + y)}^{2} - 2 y}{(x - y) (x + y)} = \frac{x^{2} + y^{2} + 2 xy - 2 y}{x^{2} - y^{2}}

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