Solve for A (complex solution)
\left\{\begin{matrix}A=\frac{BC}{B+C}\text{, }&B\neq -C\\A\in \mathrm{C}\text{, }&B=0\text{ and }C=0\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=-\frac{AC}{A-C}\text{, }&A\neq C\\B\in \mathrm{C}\text{, }&C=0\text{ and }A=0\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=\frac{BC}{B+C}\text{, }&B\neq -C\\A\in \mathrm{R}\text{, }&B=0\text{ and }C=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-\frac{AC}{A-C}\text{, }&A\neq C\\B\in \mathrm{R}\text{, }&C=0\text{ and }A=0\end{matrix}\right.
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\left(B+C\right)A=CB
Combine all terms containing A.
\left(B+C\right)A=BC
The equation is in standard form.
\frac{\left(B+C\right)A}{B+C}=\frac{BC}{B+C}
Divide both sides by B+C.
A=\frac{BC}{B+C}
Dividing by B+C undoes the multiplication by B+C.
AB+AC-CB=0
Subtract CB from both sides.
AB-CB=-AC
Subtract AC from both sides. Anything subtracted from zero gives its negation.
AB-BC=-AC
Reorder the terms.
\left(A-C\right)B=-AC
Combine all terms containing B.
\frac{\left(A-C\right)B}{A-C}=-\frac{AC}{A-C}
Divide both sides by A-C.
B=-\frac{AC}{A-C}
Dividing by A-C undoes the multiplication by A-C.
\left(B+C\right)A=CB
Combine all terms containing A.
\left(B+C\right)A=BC
The equation is in standard form.
\frac{\left(B+C\right)A}{B+C}=\frac{BC}{B+C}
Divide both sides by B+C.
A=\frac{BC}{B+C}
Dividing by B+C undoes the multiplication by B+C.
AB+AC-CB=0
Subtract CB from both sides.
AB-CB=-AC
Subtract AC from both sides. Anything subtracted from zero gives its negation.
AB-BC=-AC
Reorder the terms.
\left(A-C\right)B=-AC
Combine all terms containing B.
\frac{\left(A-C\right)B}{A-C}=-\frac{AC}{A-C}
Divide both sides by A-C.
B=-\frac{AC}{A-C}
Dividing by A-C undoes the multiplication by A-C.
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}