Solve for A (complex solution)
\left\{\begin{matrix}A=-\frac{-2Bx+7B-7}{2x+7}\text{, }&x\neq -\frac{7}{2}\\A\in \mathrm{C}\text{, }&B=\frac{1}{2}\text{ and }x=-\frac{7}{2}\end{matrix}\right.
Solve for B (complex solution)
\left\{\begin{matrix}B=-\frac{2Ax+7A-7}{7-2x}\text{, }&x\neq \frac{7}{2}\\B\in \mathrm{C}\text{, }&x=\frac{7}{2}\text{ and }A=\frac{1}{2}\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=-\frac{-2Bx+7B-7}{2x+7}\text{, }&x\neq -\frac{7}{2}\\A\in \mathrm{R}\text{, }&B=\frac{1}{2}\text{ and }x=-\frac{7}{2}\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-\frac{2Ax+7A-7}{7-2x}\text{, }&x\neq \frac{7}{2}\\B\in \mathrm{R}\text{, }&x=\frac{7}{2}\text{ and }A=\frac{1}{2}\end{matrix}\right.
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2Ax+7A+B\left(7-2x\right)=7
Use the distributive property to multiply A by 2x+7.
2Ax+7A+7B-2Bx=7
Use the distributive property to multiply B by 7-2x.
2Ax+7A-2Bx=7-7B
Subtract 7B from both sides.
2Ax+7A=7-7B+2Bx
Add 2Bx to both sides.
\left(2x+7\right)A=7-7B+2Bx
Combine all terms containing A.
\left(2x+7\right)A=2Bx-7B+7
The equation is in standard form.
\frac{\left(2x+7\right)A}{2x+7}=\frac{2Bx-7B+7}{2x+7}
Divide both sides by 2x+7.
A=\frac{2Bx-7B+7}{2x+7}
Dividing by 2x+7 undoes the multiplication by 2x+7.
2Ax+7A+B\left(7-2x\right)=7
Use the distributive property to multiply A by 2x+7.
2Ax+7A+7B-2Bx=7
Use the distributive property to multiply B by 7-2x.
7A+7B-2Bx=7-2Ax
Subtract 2Ax from both sides.
7B-2Bx=7-2Ax-7A
Subtract 7A from both sides.
\left(7-2x\right)B=7-2Ax-7A
Combine all terms containing B.
\left(7-2x\right)B=7-7A-2Ax
The equation is in standard form.
\frac{\left(7-2x\right)B}{7-2x}=\frac{7-7A-2Ax}{7-2x}
Divide both sides by 7-2x.
B=\frac{7-7A-2Ax}{7-2x}
Dividing by 7-2x undoes the multiplication by 7-2x.
2Ax+7A+B\left(7-2x\right)=7
Use the distributive property to multiply A by 2x+7.
2Ax+7A+7B-2Bx=7
Use the distributive property to multiply B by 7-2x.
2Ax+7A-2Bx=7-7B
Subtract 7B from both sides.
2Ax+7A=7-7B+2Bx
Add 2Bx to both sides.
\left(2x+7\right)A=7-7B+2Bx
Combine all terms containing A.
\left(2x+7\right)A=2Bx-7B+7
The equation is in standard form.
\frac{\left(2x+7\right)A}{2x+7}=\frac{2Bx-7B+7}{2x+7}
Divide both sides by 2x+7.
A=\frac{2Bx-7B+7}{2x+7}
Dividing by 2x+7 undoes the multiplication by 2x+7.
2Ax+7A+B\left(7-2x\right)=7
Use the distributive property to multiply A by 2x+7.
2Ax+7A+7B-2Bx=7
Use the distributive property to multiply B by 7-2x.
7A+7B-2Bx=7-2Ax
Subtract 2Ax from both sides.
7B-2Bx=7-2Ax-7A
Subtract 7A from both sides.
\left(7-2x\right)B=7-2Ax-7A
Combine all terms containing B.
\left(7-2x\right)B=7-7A-2Ax
The equation is in standard form.
\frac{\left(7-2x\right)B}{7-2x}=\frac{7-7A-2Ax}{7-2x}
Divide both sides by 7-2x.
B=\frac{7-7A-2Ax}{7-2x}
Dividing by 7-2x undoes the multiplication by 7-2x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
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}