Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{x^{2}-3x+6y}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\f\in \mathrm{C}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=\frac{x\left(3-x\right)}{6}\text{ and }g=0\text{ and }x\neq 0\right)\end{matrix}\right.
Solve for g (complex solution)
\left\{\begin{matrix}g=\frac{x^{2}-3x+6y}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{C}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=\frac{x\left(3-x\right)}{6}\text{ and }f=0\text{ and }x\neq 0\right)\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{x^{2}-3x+6y}{gx}\text{, }&x\neq 0\text{ and }g\neq 0\\f\in \mathrm{R}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=\frac{x\left(3-x\right)}{6}\text{ and }g=0\text{ and }x\neq 0\right)\end{matrix}\right.
Solve for g
\left\{\begin{matrix}g=\frac{x^{2}-3x+6y}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\g\in \mathrm{R}\text{, }&\left(y=0\text{ and }x=0\right)\text{ or }\left(y=\frac{x\left(3-x\right)}{6}\text{ and }f=0\text{ and }x\neq 0\right)\end{matrix}\right.
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gxf=x^{2}-3x+6y
The equation is in standard form.
\frac{gxf}{gx}=\frac{x^{2}-3x+6y}{gx}
Divide both sides by gx.
f=\frac{x^{2}-3x+6y}{gx}
Dividing by gx undoes the multiplication by gx.
fxg=x^{2}-3x+6y
The equation is in standard form.
\frac{fxg}{fx}=\frac{x^{2}-3x+6y}{fx}
Divide both sides by fx.
g=\frac{x^{2}-3x+6y}{fx}
Dividing by fx undoes the multiplication by fx.
gxf=x^{2}-3x+6y
The equation is in standard form.
\frac{gxf}{gx}=\frac{x^{2}-3x+6y}{gx}
Divide both sides by gx.
f=\frac{x^{2}-3x+6y}{gx}
Dividing by gx undoes the multiplication by gx.
fxg=x^{2}-3x+6y
The equation is in standard form.
\frac{fxg}{fx}=\frac{x^{2}-3x+6y}{fx}
Divide both sides by fx.
g=\frac{x^{2}-3x+6y}{fx}
Dividing by fx undoes the multiplication by fx.
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