Question

Simplifique as seguintes expressoes algebricas
$\frac{x^{-1} + y^{-1} }{x^{-2}- y^{-2} }$

Answer 1

Explicação passo-a-passo:

$\frac{ {x}^{ - 1} + {y}^{ - 1} }{ {x}^{ - 2} - {y}^{ - 2} }$

$= \frac{ \frac{1}{x} + \frac{1}{y} }{ \frac{1}{ {x}^{2} } - \frac{1}{ {y}^{2} } }$

$= \frac{ \frac{y + x}{xy} }{ \frac{ {y}^{2} - {x}^{2} }{ {x}^{2} {y}^{2} } }$

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

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

$= \frac{(x + y)(xy)(xy)}{(xy)(y + x)(y - x) }$

$= \frac{xy}{y - x}$