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