Shown below are the steps a student took to solve the simple interest formula [tex]A = P(1 + rt)[/tex] for [tex]r[/tex].
[tex]\[
\begin{array}{l}
A = P(1 + rt) \\
A = P + rt \\
A - P = rt \\
r = \frac{A - P}{t}
\end{array}
\][/tex]
Explain the algebraic error in the student's work. Then, state how the equation [tex]r = \frac{A - P}{t}[/tex] can be modified to produce the correct result.