Solve for A (complex solution)
\left\{\begin{matrix}A=-B+\frac{R}{x}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&R=0\text{ and }x=0\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=-A+\frac{R}{x}\text{, }&x\neq 0\\B\in \mathrm{C}\text{, }&R=0\text{ and }x=0\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=-B+\frac{R}{x}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&R=0\text{ and }x=0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-A+\frac{R}{x}\text{, }&x\neq 0\\B\in \mathrm{R}\text{, }&R=0\text{ and }x=0\end{matrix}\right.
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R=xA+xB
Use the distributive property to multiply x by A+B.
xA+xB=R
Swap sides so that all variable terms are on the left hand side.
xA=R-xB
Subtract xB from both sides.
xA=R-Bx
The equation is in standard form.
\frac{xA}{x}=\frac{R-Bx}{x}
Divide both sides by x.
A=\frac{R-Bx}{x}
Dividing by x undoes the multiplication by x.
A=-B+\frac{R}{x}
Divide R-Bx by x.
R=xA+xB
Use the distributive property to multiply x by A+B.
xA+xB=R
Swap sides so that all variable terms are on the left hand side.
xB=R-xA
Subtract xA from both sides.
xB=R-Ax
The equation is in standard form.
\frac{xB}{x}=\frac{R-Ax}{x}
Divide both sides by x.
B=\frac{R-Ax}{x}
Dividing by x undoes the multiplication by x.
B=-A+\frac{R}{x}
Divide R-Ax by x.
R=xA+xB
Use the distributive property to multiply x by A+B.
xA+xB=R
Swap sides so that all variable terms are on the left hand side.
xA=R-xB
Subtract xB from both sides.
xA=R-Bx
The equation is in standard form.
\frac{xA}{x}=\frac{R-Bx}{x}
Divide both sides by x.
A=\frac{R-Bx}{x}
Dividing by x undoes the multiplication by x.
A=-B+\frac{R}{x}
Divide R-Bx by x.
R=xA+xB
Use the distributive property to multiply x by A+B.
xA+xB=R
Swap sides so that all variable terms are on the left hand side.
xB=R-xA
Subtract xA from both sides.
xB=R-Ax
The equation is in standard form.
\frac{xB}{x}=\frac{R-Ax}{x}
Divide both sides by x.
B=\frac{R-Ax}{x}
Dividing by x undoes the multiplication by x.
B=-A+\frac{R}{x}
Divide R-Ax by x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}