Question 109615
(x^-1 - y^-1)^-1
:
The reciprocal eliminates the negative on the exponent, then (in this case) it's 1 so it can be ignored.
:
{{{(1/x - 1/y)^-1}}} = {{{1/((1/x - 1/y))}}} = {{{1/((y-x)/(xy))}}} make the denominator into a single fraction:
:
Invert the dividing fraction and multiply
1 *  {{{(xy)/((y-x))}}} = {{{(xy)/((y-x))}}}
:
Did the make sense to you? Any questions?