Answer
$q=\frac{pf}{p-f}$
Work Step by Step
Eliminate the fractions by multiplying the LCD $pqf$ to both sides of the equation:
$$\require{cancel}
(pqf) \cdot \left(\frac{1}{p} + \frac{1}{q}\right)=(pqf)(\frac{1}{f})
\\(pqf) \cdot \left(\frac{1}{p} + \frac{1}{q}\right)=pq$$
Distribute $pqf$:
$$pqf(\frac{1}{p}) + pqf(\frac{1}{q})=pq
\\\frac{pqf}{p} + \frac{pqf}{q}=pq
\\qf+pf=pq$$
Subtract $(qf)$ from both sides:
$$qf+pf-qf=pq-qf
\\pf=pq-qf$$
Factor out $q$:
$$pf=q(p-f)$$
Divide $p-f$ to both sides of the equation:
$$\frac{pf}{p-f}=\frac{q(p-f)}{p-f}
\\\frac{pf}{p-f}=q$$
