Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$t=\dfrac{rs}{q-r}$
Using the properties of equality, in terms of $t$, the given expression, $qt=r(s+t)$, is equivalent to \begin{array}{l} qt=rs+rt \\\\ qt-rt=rs \\\\ t(q-r)=rs \\\\ t=\dfrac{rs}{q-r} .\end{array}