Question

упростите выражение (у/ху-х²+х/ху-у²): х²+2ху+у²/1/х +1/у
Помогите пожалуйста. Спасибо

Answer 1

$( \frac{y}{xy - {x}^{2} } + \frac{x}{xy - {y}^{2} } ) \div \frac{ {x}^{2} + 2xy + {y}^{2} }{ \frac{1}{x} + \frac{1}{y} } = ( \frac{y}{x(y - x)} + \frac{x}{y(x - y)} ) \div \frac{ {(x + y)}^{2} }{ \frac{y + x}{xy} } = ( - \frac{y}{x(x - y)} + \frac{x}{y(x - y)} )\div ((x + y) \times xy) = \frac{ {x}^{2} - {y}^{2} }{xy(x - y)} \times \frac{1}{xy(x + y)} = \frac{(x - y)(x + y)}{ {x}^{2} {y}^{2} (x - y)(x + y) } = \frac{1}{ {x}^{2} {y}^{2} }$