Hasil dari : - Universityku

$rm{left( {x}^{ - 1} + {y}^{ - 1} right) }^{ - 1} left( {x}^{ - 2} - {y}^{ - 2} right)$
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dapat dinyatakan sebagai

a. (x-y)/(xy)
b. (y-x)/(xy)
c. (xy)/(x+y)
d. (xy)/(x-y)
e. (xy)/(y-x)

Hasil dari :

$= {( {x}^{ - 1} + {y}^{ - 1} )}^{ - 1} times ( {x}^{ - 2} - {y}^{ - 2} )$

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

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

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

$= frac{ cancel{xy}}{y + x} times frac{(y + x)(y - x)}{ cancel{(xy)}.(xy)}$

$= frac{1}{ cancel{y + x}} times frac{ cancel{(y + x)}(y - x)}{xy}$

$= frac{1}{1} times frac{y - x}{xy}$

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

Jawabannya yang B.

Jawab:

Penjelasan dengan langkah-langkah:

$rm{left( {x}^{ - 1} + {y}^{ - 1} right) }^{ - 1} left( {x}^{ - 2} - {y}^{ - 2} right) = dfrac{x^{-2}-y^{-2} }{x^{-1}+y^{-1} }\rm{left( {x}^{ - 1} + {y}^{ - 1} right) }^{ - 1} left( {x}^{ - 2} - {y}^{ - 2} right) = dfrac{(x^{-1}-y^{-1})(x^{-1}+y^{-1}) }{x^{-1}+y^{-1} } = x^{-1}-y^{-1}\\boxed{boxed{rm{left( {x}^{ - 1} + {y}^{ - 1} right) }^{ - 1} left( {x}^{ - 2} - {y}^{ - 2} right) = dfrac{1}{x}-dfrac{1}{y} = dfrac{y-x}{xy} }}$