Question

Simplifique a expressão algébrica.​

Answer 1

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