[tex]\frac{\frac{1}{xy}}{\frac{1}{x} - \frac{1}{y}}[/tex]
for bottom, Get common denominator between the two of them [tex]\frac{1}{x} - \frac{1}{y}[/tex]
Multiply 1/x top and bottom by y/y, multiply 1/y tom and bottom by x/x and you have [tex]\frac{1*y}{x*y} - \frac{1*x}{y*x} = \frac{y-x}{xy}[/tex] so now original is [tex]\frac{\frac{1}{xy}}{\frac{y-x}{xy}}[/tex]
multiply top and bottom by xy [tex]\frac{\frac{1}{xy} * xy}{\frac{y-x}{xy} * xy} = \frac{1}{y-x}[/tex]
your answer is [tex]\frac{1}{y-x}[/tex]
