#### Answer

$f=\frac{pq}{q+p}$

#### Work Step by Step

Multiply all terms by the LCD. Then factor out $f$ from $qf+pf$ and divide both sides by $q+p$.
$\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$ for $f$
$pqf(\frac{1}{p}+\frac{1}{q})=\frac{1}{f}(pqf)$
$qf+pf=pq$
$f(q+p)=pq$
$f=\frac{pq}{q+p}$