How do you simplify $[x^-1+y^-1]/[x^-2-y^-2]$ ?

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Answer 1 · 2016-07-25T18:37:39

$x-y$

This one is interesting in that its set to look tricky but its not really that bad as it seems.

Firs we know that $z^-x = 1/(z^x)$ and also $z^-(-x) = 1/(z^-x) = z^x$

so lets rearrange this equation

$(x^2-y^2)/(x^1+y^1)$

now it turns out that
$(x-y)(x+y) = (x^2-y^2)$

so we have
$((x-y)cancel(x+y))/ cancel(x+y)$

How do you simplify [x^-1+y^-1]/[x^-2-y^-2][x^-1+y^-1]/[x^-2-y^-2]?