Solve for B
\left\{\begin{matrix}B=\frac{S+\beta }{S}\text{, }&S\neq 0\\B\in \mathrm{R}\text{, }&S=0\text{ and }\beta =0\end{matrix}\right.
Solve for S
\left\{\begin{matrix}S=\frac{\beta }{B-1}\text{, }&B\neq 1\\S\in \mathrm{R}\text{, }&\beta =0\text{ and }B=1\end{matrix}\right.
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SB=S+\beta
The equation is in standard form.
\frac{SB}{S}=\frac{S+\beta }{S}
Divide both sides by S.
B=\frac{S+\beta }{S}
Dividing by S undoes the multiplication by S.
SB-S=\beta
Subtract S from both sides.
\left(B-1\right)S=\beta
Combine all terms containing S.
\frac{\left(B-1\right)S}{B-1}=\frac{\beta }{B-1}
Divide both sides by B-1.
S=\frac{\beta }{B-1}
Dividing by B-1 undoes the multiplication by B-1.
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