Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{2b}{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{2b}{x}-3\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.
Solve for b
b=\frac{x\left(a+3\right)}{2}
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2b-ax=3x
Swap sides so that all variable terms are on the left hand side.
-ax=3x-2b
Subtract 2b from both sides.
\left(-x\right)a=3x-2b
The equation is in standard form.
\frac{\left(-x\right)a}{-x}=\frac{3x-2b}{-x}
Divide both sides by -x.
a=\frac{3x-2b}{-x}
Dividing by -x undoes the multiplication by -x.
a=\frac{2b}{x}-3
Divide 3x-2b by -x.
2b-ax=3x
Swap sides so that all variable terms are on the left hand side.
-ax=3x-2b
Subtract 2b from both sides.
\left(-x\right)a=3x-2b
The equation is in standard form.
\frac{\left(-x\right)a}{-x}=\frac{3x-2b}{-x}
Divide both sides by -x.
a=\frac{3x-2b}{-x}
Dividing by -x undoes the multiplication by -x.
a=\frac{2b}{x}-3
Divide 3x-2b by -x.
2b-ax=3x
Swap sides so that all variable terms are on the left hand side.
2b=3x+ax
Add ax to both sides.
2b=ax+3x
The equation is in standard form.
\frac{2b}{2}=\frac{x\left(a+3\right)}{2}
Divide both sides by 2.
b=\frac{x\left(a+3\right)}{2}
Dividing by 2 undoes the multiplication by 2.
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}