Solve for f
\left\{\begin{matrix}f=\frac{z}{xy}\text{, }&y\neq 0\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&\left(y=0\text{ or }x=0\right)\text{ and }z=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{z}{fy}\text{, }&y\neq 0\text{ and }f\neq 0\\x\in \mathrm{R}\text{, }&\left(y=0\text{ or }f=0\right)\text{ and }z=0\end{matrix}\right.
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fxy=z
Swap sides so that all variable terms are on the left hand side.
xyf=z
The equation is in standard form.
\frac{xyf}{xy}=\frac{z}{xy}
Divide both sides by xy.
f=\frac{z}{xy}
Dividing by xy undoes the multiplication by xy.
fxy=z
Swap sides so that all variable terms are on the left hand side.
fyx=z
The equation is in standard form.
\frac{fyx}{fy}=\frac{z}{fy}
Divide both sides by fy.
x=\frac{z}{fy}
Dividing by fy undoes the multiplication by fy.
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