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prove that (x^-1/x^-1+y^-1)+ (x^-1/x^-1-y^-1)=2y²/y²-x²

Dear student

w e h a v e, (\frac{\frac{1}{x}}{\frac{1}{x} + \frac{1}{y}}) + (\frac{\frac{1}{x}}{\frac{1}{x} - \frac{1}{y}}) = (\frac{\frac{1}{x}}{\frac{x + y}{x y}}) + (\frac{\frac{1}{x}}{\frac{y - x}{x y}}) = (\frac{1}{x} \times \frac{x y}{x + y}) + (\frac{1}{x} \times \frac{x y}{y - x}) = (\frac{y}{y + x}) + (\frac{y}{y - x}) = \frac{y (y - x) + y (y + x)}{y^{2} - x^{2}} = \frac{y^{2} - x y + y^{2} + x y}{y^{2} - x^{2}} = \frac{2 y^{2}}{y^{2} - x^{2}}

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