Solve for a (complex solution)
\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=2\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}\\b=-a\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=2\end{matrix}\right.
Solve for a
\left\{\begin{matrix}\\a=-b\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=2\end{matrix}\right.
Solve for b
\left\{\begin{matrix}\\b=-a\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=2\end{matrix}\right.
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2a-ax=bx-2b
Swap sides so that all variable terms are on the left hand side.
\left(2-x\right)a=bx-2b
Combine all terms containing a.
\frac{\left(2-x\right)a}{2-x}=\frac{b\left(x-2\right)}{2-x}
Divide both sides by 2-x.
a=\frac{b\left(x-2\right)}{2-x}
Dividing by 2-x undoes the multiplication by 2-x.
a=-b
Divide b\left(-2+x\right) by 2-x.
\left(x-2\right)b=2a-ax
Combine all terms containing b.
\frac{\left(x-2\right)b}{x-2}=\frac{a\left(2-x\right)}{x-2}
Divide both sides by -2+x.
b=\frac{a\left(2-x\right)}{x-2}
Dividing by -2+x undoes the multiplication by -2+x.
b=-a
Divide a\left(2-x\right) by -2+x.
2a-ax=bx-2b
Swap sides so that all variable terms are on the left hand side.
\left(2-x\right)a=bx-2b
Combine all terms containing a.
\frac{\left(2-x\right)a}{2-x}=\frac{b\left(x-2\right)}{2-x}
Divide both sides by 2-x.
a=\frac{b\left(x-2\right)}{2-x}
Dividing by 2-x undoes the multiplication by 2-x.
a=-b
Divide b\left(-2+x\right) by 2-x.
\left(x-2\right)b=2a-ax
Combine all terms containing b.
\frac{\left(x-2\right)b}{x-2}=\frac{a\left(2-x\right)}{x-2}
Divide both sides by -2+x.
b=\frac{a\left(2-x\right)}{x-2}
Dividing by -2+x undoes the multiplication by -2+x.
b=-a
Divide a\left(2-x\right) by -2+x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}