Question

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

Answer 1

`x-y`

Explanation:

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)`