Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{a}{x}+3\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
Solve for a
a=x\left(f-3\right)
Solve for f
\left\{\begin{matrix}f=\frac{a}{x}+3\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }a=0\end{matrix}\right.
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xf=3x+a
The equation is in standard form.
\frac{xf}{x}=\frac{3x+a}{x}
Divide both sides by x.
f=\frac{3x+a}{x}
Dividing by x undoes the multiplication by x.
f=\frac{a}{x}+3
Divide 3x+a by x.
3x+a=fx
Swap sides so that all variable terms are on the left hand side.
a=fx-3x
Subtract 3x from both sides.
xf=3x+a
The equation is in standard form.
\frac{xf}{x}=\frac{3x+a}{x}
Divide both sides by x.
f=\frac{3x+a}{x}
Dividing by x undoes the multiplication by x.
f=\frac{a}{x}+3
Divide 3x+a by x.
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