Question

$( \frac{x + y}{y} - \frac{x}{x + y} ) \div ( \frac{x + y}{x} - \frac{y}{x + y} ) = \frac{x}{y}$
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Answer 1

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

Что и требовалось доказать