Question 991924
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{{{1/x}}} + {{{1/y}}} = {{{y/(xy)}}} + {{{x/(xy)}}} = {{{(y+x)/(xy)}}}.


{{{1/x}}} - {{{1/y}}} = {{{y/(xy)}}} - {{{x/(xy)}}} = {{{(y-x)/(xy)}}}.


Therefore,


{{{(1/x + 1/y)/(1/x - 1/y)}}} = {{{((y+x)/(xy))/((y-x)/(xy))}}} = {{{((y+x)*(xy))/((y-x)*(xy))}}} = {{{(y+x)/(y-x)}}}.