Question 749119
{{{(x^-1+y^-1)^-1=1/(x^-1+y^-1)=1/((1/x)+(1/y))}}}


At the lower level, focus on the main denominator.  Lowest Common Denominator of the main denominator is xy.  Try this:  Multiply the whole complex fraction by {{{(xy)/(xy)}}}.  That should give you something which simplifies neatly into a noncomplex fraction.


{{{(1/((1/x)+(1/y)))*((xy)/(xy))}}}
{{{xy/(xy/x+xy/y)}}}
{{{highlight(xy/(y+x))}}}