Answer
$t=\frac{rK}{r+K}$
Work Step by Step
Multiply $r-t$ to both sides of the equation:
$$\require{cancel}
(r-t) \cdot K=(r-t)\cdot \frac{rt}{r-t}
\\(r-t) \cdot K=\cancel{(r-t)}\cdot \frac{rt}{\cancel{r-t}}
\\rK-tK=rt$$
Add $tK$ to both sides:
$$rK-tK+tK=rt+tK
\\rK=rt+tK$$
Factor out $t$:
$$rK=t(r+K)$$
Divide $(r+K)$ to both sides:
$\frac{rK}{r+K}=\frac{t(r+K)}{r+K}
\\\frac{rK}{r+K}=t$