Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{y+3}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&y=-3\text{ and }x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{y+3}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&y=-3\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-f^{-\frac{1}{2}}\sqrt{y+3}\text{; }x=f^{-\frac{1}{2}}\sqrt{y+3}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=-3\text{ and }f=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\sqrt{\frac{y+3}{f}}\text{; }x=-\sqrt{\frac{y+3}{f}}\text{, }&\left(y\geq -3\text{ and }f>0\right)\text{ or }\left(y\leq -3\text{ and }f<0\right)\\x\in \mathrm{R}\text{, }&y=-3\text{ and }f=0\end{matrix}\right.
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fx^{2}-3=y
Swap sides so that all variable terms are on the left hand side.
fx^{2}=y+3
Add 3 to both sides.
x^{2}f=y+3
The equation is in standard form.
\frac{x^{2}f}{x^{2}}=\frac{y+3}{x^{2}}
Divide both sides by x^{2}.
f=\frac{y+3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
fx^{2}-3=y
Swap sides so that all variable terms are on the left hand side.
fx^{2}=y+3
Add 3 to both sides.
x^{2}f=y+3
The equation is in standard form.
\frac{x^{2}f}{x^{2}}=\frac{y+3}{x^{2}}
Divide both sides by x^{2}.
f=\frac{y+3}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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