Question

$frac{x}{y}( frac{y}{x}- frac{x}{y}( frac{y^2}{x^2}- frac{x}{y}( frac{y^3}{x^3}- frac{y^4}{x^4})))$

Решите пожалуйста

Answer 1

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

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

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