start by dividing by p on both sides
[tex]\begin{gathered} \frac{S}{P}=\frac{P}{P}(1+rt) \\ \frac{S}{P}=1+rt \end{gathered}[/tex]substract 1 on both sides
[tex]\begin{gathered} \frac{S}{P}-1=1+rt-1 \\ \frac{S}{P}-1=rt \end{gathered}[/tex]Divide by t on both sides to solve for r
[tex]\begin{gathered} (\frac{S}{P}-1)(\frac{1}{t})=\frac{rt}{t} \\ \frac{S}{Pt}-\frac{1}{t}=r \end{gathered}[/tex]ANSWER
[tex]r=\frac{S}{Pt}-\frac{1}{t}[/tex]