Chapter 6 - Section 6.6 - Rational Equations and Problem Solving - Exercise Set - Page 387: 13

$f_2=-\dfrac{ff_1}{f-f_1}$

Using the properties of equality, in terms of $ f_2 ,$ the given equation, $ f=\dfrac{f_1f_2}{f_1+f_2} ,$ is equivalent to \begin{array}{l} f(f_1+f_2)=f_1f_2 \\\\ ff_1+ff_2=f_1f_2 \\\\ ff_2-f_1f_2=-ff_1 \\\\ f_2(f-f_1)=-ff_1 \\\\ f_2=-\dfrac{ff_1}{f-f_1} .\end{array}