Answer
$f_{2}=\displaystyle \frac{ff_{1}}{f_{1}-f}$
Work Step by Step
Get rid of fractions, multiply with LCD=$(f_{1}+f_{2})$
$ f(f_{1}+f_{2})=f_{1}f_{2}\qquad$ ... distribute
$ ff_{1}+ff_{2}=f_{1}f_{2}\qquad$ ... add $-ff_{2}$
$ ff_{1}=f_{1}f_{2}-ff_{2}\qquad$ ... factor out $f_{2}$
$ ff_{1}=f_{2}(f_{1}-f)\qquad$ ...divide with $(f_{1}-f)$ to isolate $f_{1}$
$\displaystyle \frac{ff_{1}}{f_{1}-f}=f_{2}$
$f_{2}=\displaystyle \frac{ff_{1}}{f_{1}-f}$
