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\[\frac{ \frac{ 1 }{ x }- \frac{ 1 }{ y} }{ \frac{ 1 }{ x ^{2} }- \frac{ 1 }{ y ^{2}} }\]
what do you need to know
is their any choices?
\[\frac{ 1 }{ x }-\frac{ 1 }{ y } = \frac{ y-x }{ xy }\] \[\frac{ 1 }{ x^2 }-\frac{ 1 }{ y^2 } = \frac{ y^2-x^2 }{ x^2y^2 }\] \[\frac{ \frac{ y-x }{ xy } }{ \frac{ y^2-x^2 }{ x^2y^2 } } = \frac{ x^2y^2 }{ y^2-x^2 } * \frac{ y-x }{ xy }\] \[y^2-x^2 = (y-x)(y+x)\] so... (xy) cancels and (y-x) cancels this leaves. \[\frac{ xy }{ y+x }\]
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np!
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