Solve for D_x (complex solution)
\left\{\begin{matrix}D_{x}=\frac{x^{2}+2}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\D_{x}\in \mathrm{C}\text{, }&\left(x=\sqrt{2}i\text{ or }x=-\sqrt{2}i\right)\text{ and }f=0\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{x^{2}+2}{D_{x}x}\text{, }&x\neq 0\text{ and }D_{x}\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\sqrt{2}i\text{ or }x=-\sqrt{2}i\right)\text{ and }D_{x}=0\end{matrix}\right.
Solve for D_x
D_{x}=\frac{x^{2}+2}{fx}
x\neq 0\text{ and }f\neq 0
Solve for f
f=\frac{x^{2}+2}{D_{x}x}
x\neq 0\text{ and }D_{x}\neq 0
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fxD_{x}=x^{2}+2
The equation is in standard form.
\frac{fxD_{x}}{fx}=\frac{x^{2}+2}{fx}
Divide both sides by fx.
D_{x}=\frac{x^{2}+2}{fx}
Dividing by fx undoes the multiplication by fx.
D_{x}xf=x^{2}+2
The equation is in standard form.
\frac{D_{x}xf}{D_{x}x}=\frac{x^{2}+2}{D_{x}x}
Divide both sides by D_{x}x.
f=\frac{x^{2}+2}{D_{x}x}
Dividing by D_{x}x undoes the multiplication by D_{x}x.
fxD_{x}=x^{2}+2
The equation is in standard form.
\frac{fxD_{x}}{fx}=\frac{x^{2}+2}{fx}
Divide both sides by fx.
D_{x}=\frac{x^{2}+2}{fx}
Dividing by fx undoes the multiplication by fx.
D_{x}xf=x^{2}+2
The equation is in standard form.
\frac{D_{x}xf}{D_{x}x}=\frac{x^{2}+2}{D_{x}x}
Divide both sides by D_{x}x.
f=\frac{x^{2}+2}{D_{x}x}
Dividing by D_{x}x undoes the multiplication by D_{x}x.
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