Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{r-y-x^{r}}{x}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&y=r\text{ and }x=0\end{matrix}\right.
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-x^{r}-fx+r=y
Swap sides so that all variable terms are on the left hand side.
-fx+r=y+x^{r}
Add x^{r} to both sides.
-fx=y+x^{r}-r
Subtract r from both sides.
\left(-x\right)f=x^{r}+y-r
The equation is in standard form.
\frac{\left(-x\right)f}{-x}=\frac{x^{r}+y-r}{-x}
Divide both sides by -x.
f=\frac{x^{r}+y-r}{-x}
Dividing by -x undoes the multiplication by -x.
f=-\frac{x^{r}+y-r}{x}
Divide y+x^{r}-r by -x.
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