Помогите решить пожалуйста. [latex]\frac{x}{y} (\frac{y}{x} - \frac{x}{y} (\frac{y^2}{x^2} - \frac{x}{y} ( \frac{y^3}{x^3} - \frac{y^4}{x^4} )))[/latex]Ответ должен выйти: [latex]\frac{x-y}{x}[/latex] 

[latex] \frac{x}{y} *( \frac{y}{x} - \frac{x}{y} ( \frac{y ^{2} }{ x^{2} } - \frac{x}{y} ( \frac{ y^{3} }{ x^{3} } - \frac{y ^{4} }{ x^{4} } )))= \frac{x-y}{y} [/latex] [latex]1) \frac{y ^{3} }{ x^{3} } - \frac{y ^{4} }{ x^{4} } = \frac{xy ^{3}-y ^{4} }{ x^{4} } = \frac{y ^{3} (x-y)}{ x^{4} } \\ \\ 2) \frac{x}{y} * \frac{y ^{3}(x-y) }{ x^{4} } = \frac{y ^{2}(x-y) }{ x^{3} } = \frac{xy ^{2} -y ^{3} }{ x^{3} } \\ \\ 3) \frac{y ^{2} }{ x^{2} } - \frac{xy ^{2}-y ^{3} }{ x^{3} } = \frac{xy ^{2}-xy ^{2}+y ^{3}}{ x^{3} }= \frac{y ^{3} }{ x^{2} } \\ \\ 4) \frac{x}{y} * \frac{y ^{3} }{ x^{3} } = \frac{y ^{2} }{ x^{2} } \\ \\ [/latex] [latex]5) \frac{y}{x} - \frac{y ^{2} }{ x^{2} } = \frac{xy-y ^{2} }{ x^{2} } = \frac{y(x-y)}{ x^{2} } \\ \\ 6) \frac{x}{y} * \frac{y(x-y)}{ x^{2} } = \frac{x-y}{x} [/latex]