tex] Решите пожалуйста...

Сырок2002 @Сырок2002

August 2022 1 4 Report

[tex] \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}))) [/tex]

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$\frac{x}{y}\cdot \Big (\frac{y}{x}-\frac{x}{y}\cdot \Big (\frac{y^2}{x^2}-\frac{x}{y}\cdot \Big (\frac{y^3}{x^3}-\frac{y^4}{x^4}\Big )\Big )\Big )=\\\\=\frac{x}{y} \cdot \Big (\frac{y}{x}-\frac{x}{y}\cdot \Big (\frac{y^2}{x^2}-\frac{x}{y}\cdot \frac{xy^3-y^4}{x^4}\Big )\Big )=\\\\=\frac{x}{y}\cdot \Big ( \frac{y}{x}-\frac{x}{y} \cdot \Big (\frac{y^2}{x^2}-\frac{x\cdot y^3(x-y)}{y\cdot x^4} \Big )\Big )=$

$=\frac{x}{y}\cdot \Big (\frac{y}{x}-\frac{x}{y}\cdot \Big (\frac{y^2}{x^2}- \frac{y^2(x-y)}{x^3}\Big )\Big )=$

$= \frac{x}{y}\cdot \Big (\frac{y}{x}-\frac{x}{y}\cdot \frac{xy^2-xy^2+y^3}{x^3}\Big )=\frac{x}{y}\cdot \Big (\frac{y}{x}-\frac{x}{y}\cdot \frac{y^3}{x^3}\Big )=\\\\=\frac{x}{y}\cdot \Big (\frac{y}{x}-\frac{y^2}{x^2}\Big )=\frac{x}{y}\cdot \frac{xy-y^2}{x^2}= \frac{x}{y}\cdot \frac{y\cdot (x-y)}{x^2} = \frac{x-y}{x} =1- \frac{y}{x}$

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