[tex]\frac{1}{f_{r}} + \frac{1}{f_{s}} = \frac{1}{x} + \frac{1}{y}\\\\\frac{1}{f_{r}} = \frac{1}{x}+\frac{1}{y}-\frac{1}{f_{s}}\\\\\frac{1}{f_{r}} = \frac{yf_{s}+xf_{s}-xy}{xyf_{s}}\\\\\frac{1}{f_{r}} = \frac{f_{s}(x+y)-xy}{xyf_{s}}\\\\f_{r} = \frac{xyf_{s}}{f_{s}(x+y)-xy}[/tex]
