Sederhanakan pecahan berikut

$( frac{ frac{x}{y} - frac{y}{x} }{ {x}^{2} - {y}^{2} } )$
$a - frac{1}{xy} \ b frac{1}{xy} \ c frac{1}{x} \ d frac{1}{y}$

Sederhanakan pecahan berikut

Jawab:

$frac{1}{xy}$ (B)

Penjelasan dengan langkah-langkah:

$frac{frac{x}{y}-frac{y}{x} }{x^{2} -y^{2} } = frac{frac{x*x }{y*x}-frac{y*y}{x*y} }{x^{2} -y^{2} }$

= $frac{frac{x^{2} }{x*y}-frac{y^{2} }{x*y} }{x^{2} -y^{2} }$

= $frac{frac{x^{2} -y^{2}}{x*y} }{x^{2} -y^{2} }$

= $frac{x^{2} -y^{2}}{x*y} } : ({x^{2} -y^{2} )$

= $frac{x^{2} -y^{2}}{x*y} } * frac{1}{x^{2} -y^{2} }$

= $frac{1}{x*y}$

= $frac{1}{xy}$