[latex] (\frac{ x^{2} + y^{2} }{ x^{2} - y^{2} } ) ^{2} : ([/latex][latex] (\frac{x+y}{x-y} + \frac{x}{y} )[/latex][latex]* (\frac{x+y}{x-y} - \frac{y}{x}) [/latex])

Question

[latex] (\frac{ x^{2} + y^{2} }{ x^{2} - y^{2} } ) ^{2} : ([/latex][latex] (\frac{x+y}{x-y} + \frac{x}{y} )[/latex][latex]* (\frac{x+y}{x-y} - \frac{y}{x}) [/latex])

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Ответ(ы) на вопрос:

Accepted Answer

1)(x+y)/(x-y)+x/y=(xy+y²+x²-xy)/y(x-y)=(x²+y²)/y(x-y) 2)(x+y)/(x-y)-y/x=(x²+xy-xy+y²)/x(x-y)=(x²+y²)/x(x-y) 3)(x²+y²)/y(x-y) *(x²+y²)/x(x-y)=(x²+y²)²/xy(x-y)² 4)(x²+y²)²/(x²-y²)² : (x²+y²)²/xy(x-y)²= (x²+y²)²/(x-y)² (x+y)² *xy(x-y)/(x²+y²)²=xy/(x+y)²