Solve for f
\left\{\begin{matrix}f=\frac{i\left(-y+\sqrt[3]{x-2}\right)}{r}\text{, }&r\neq 0\\f\in \mathrm{C}\text{, }&y=\sqrt[3]{x-2}\text{ and }r=0\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=\frac{i\left(-y+\sqrt[3]{x-2}\right)}{f}\text{, }&f\neq 0\\r\in \mathrm{C}\text{, }&y=\sqrt[3]{x-2}\text{ and }f=0\end{matrix}\right.
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y=\sqrt[3]{x-2}+ifr
Multiply 1 and i to get i.
\sqrt[3]{x-2}+ifr=y
Swap sides so that all variable terms are on the left hand side.
ifr=y-\sqrt[3]{x-2}
Subtract \sqrt[3]{x-2} from both sides.
irf=y-\sqrt[3]{x-2}
The equation is in standard form.
\frac{irf}{ir}=\frac{y-\sqrt[3]{x-2}}{ir}
Divide both sides by ir.
f=\frac{y-\sqrt[3]{x-2}}{ir}
Dividing by ir undoes the multiplication by ir.
f=-\frac{i\left(y-\sqrt[3]{x-2}\right)}{r}
Divide y-\sqrt[3]{x-2} by ir.
y=\sqrt[3]{x-2}+ifr
Multiply 1 and i to get i.
\sqrt[3]{x-2}+ifr=y
Swap sides so that all variable terms are on the left hand side.
ifr=y-\sqrt[3]{x-2}
Subtract \sqrt[3]{x-2} from both sides.
\frac{ifr}{if}=\frac{y-\sqrt[3]{x-2}}{if}
Divide both sides by if.
r=\frac{y-\sqrt[3]{x-2}}{if}
Dividing by if undoes the multiplication by if.
r=-\frac{i\left(y-\sqrt[3]{x-2}\right)}{f}
Divide y-\sqrt[3]{x-2} by if.
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