Answer
$\color{blue}{r=\frac{A-P}{P}}$
Work Step by Step
Use the rule $\frac{a}{b}=\frac{c}{d}\longrightarrow ad=bc$ to obtain:
$$P(1+r)=A
\\P(1)+P(r)=A
\\P+Pr=A$$
Subtract $P$ from both sides to obtain:
$$P+Pr-P=A-P
\\Pr=A-P$$
Divide $P$ to both sides:
$$\frac{Pr}{P}=\frac{A-P}{P}
\\\color{blue}{r=\frac{A-P}{P}}$$
