Question

Помогите упростить выражение:

Answer 1

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