Solve for J
\left\{\begin{matrix}J=\frac{M}{rt+1}\text{, }&t=0\text{ or }r\neq -\frac{1}{t}\\J\in \mathrm{R}\text{, }&M=0\text{ and }r=-\frac{1}{t}\text{ and }t\neq 0\end{matrix}\right.
Solve for M
M=J\left(rt+1\right)
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J+Jrt=M
Swap sides so that all variable terms are on the left hand side.
\left(1+rt\right)J=M
Combine all terms containing J.
\left(rt+1\right)J=M
The equation is in standard form.
\frac{\left(rt+1\right)J}{rt+1}=\frac{M}{rt+1}
Divide both sides by 1+rt.
J=\frac{M}{rt+1}
Dividing by 1+rt undoes the multiplication by 1+rt.
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