Answer
$$ r= \frac{A}{Pt}-\frac{1}{t} .$$
Work Step by Step
To solve the given equation for $r$, we keep the term $ Prt$ and move out all other terms to the other side and then we divide by $Pt$ as follows:
$$ A=P+Prt \Longrightarrow Prt=A-P\Longrightarrow \frac{Prt}{Pt}=\frac{A-P}{Pt} \\ \Longrightarrow r=\frac{A-P}{Pt} =\frac{A}{Pt}-\frac{1}{t} .$$
