Answer
$f_{1}=-\dfrac{f_{2}f}{f-f_{2}}$
Work Step by Step
$f=\dfrac{f_{1}f_{2}}{f_{1}+f_{2}}$ $;$ Solve for $f_{1}$
Take $f_{1}+f_{2}$ to multiply the left side of the equation:
$f(f_{1}+f_{2})=f_{1}f_{2}$
$f_{1}f+f_{2}f=f_{1}f_{2}$
Take $f_{1}f_{2}$ to the left side and $f_{2}f$ to the right side:
$f_{1}f-f_{1}f_{2}=-f_{2}f$
Take out common factor $f_{1}$ from the left side:
$f_{1}(f-f_{2})=-f_{2}f$
Take $f-f_{2}$ to divide the right side:
$f_{1}=-\dfrac{f_{2}f}{f-f_{2}}$
