Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{bx-2x+3}{x+b}\text{, }&x\neq -b\\a\in \mathrm{C}\text{, }&\left(x=1\text{ and }b=-1\right)\text{ or }\left(x=-3\text{ and }b=3\right)\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{3-2x-ax}{x-a}\text{, }&x\neq a\\b\in \mathrm{C}\text{, }&\left(x=1\text{ and }a=1\right)\text{ or }\left(x=-3\text{ and }a=-3\right)\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{bx-2x+3}{x+b}\text{, }&x\neq -b\\a\in \mathrm{R}\text{, }&\left(x=1\text{ and }b=-1\right)\text{ or }\left(x=-3\text{ and }b=3\right)\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{3-2x-ax}{x-a}\text{, }&x\neq a\\b\in \mathrm{R}\text{, }&\left(x=1\text{ and }a=1\right)\text{ or }\left(x=-3\text{ and }a=-3\right)\end{matrix}\right.
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x^{2}+xb-ax-ab=\left(x-1\right)\left(x+3\right)
Use the distributive property to multiply x-a by x+b.
x^{2}+xb-ax-ab=x^{2}+2x-3
Use the distributive property to multiply x-1 by x+3 and combine like terms.
xb-ax-ab=x^{2}+2x-3-x^{2}
Subtract x^{2} from both sides.
xb-ax-ab=2x-3
Combine x^{2} and -x^{2} to get 0.
-ax-ab=2x-3-xb
Subtract xb from both sides.
\left(-x-b\right)a=2x-3-xb
Combine all terms containing a.
\left(-x-b\right)a=-bx+2x-3
The equation is in standard form.
\frac{\left(-x-b\right)a}{-x-b}=\frac{-bx+2x-3}{-x-b}
Divide both sides by -x-b.
a=\frac{-bx+2x-3}{-x-b}
Dividing by -x-b undoes the multiplication by -x-b.
a=-\frac{-bx+2x-3}{x+b}
Divide -3-xb+2x by -x-b.
x^{2}+xb-ax-ab=\left(x-1\right)\left(x+3\right)
Use the distributive property to multiply x-a by x+b.
x^{2}+xb-ax-ab=x^{2}+2x-3
Use the distributive property to multiply x-1 by x+3 and combine like terms.
xb-ax-ab=x^{2}+2x-3-x^{2}
Subtract x^{2} from both sides.
xb-ax-ab=2x-3
Combine x^{2} and -x^{2} to get 0.
xb-ab=2x-3+ax
Add ax to both sides.
\left(x-a\right)b=2x-3+ax
Combine all terms containing b.
\left(x-a\right)b=ax+2x-3
The equation is in standard form.
\frac{\left(x-a\right)b}{x-a}=\frac{ax+2x-3}{x-a}
Divide both sides by x-a.
b=\frac{ax+2x-3}{x-a}
Dividing by x-a undoes the multiplication by x-a.
x^{2}+xb-ax-ab=\left(x-1\right)\left(x+3\right)
Use the distributive property to multiply x-a by x+b.
x^{2}+xb-ax-ab=x^{2}+2x-3
Use the distributive property to multiply x-1 by x+3 and combine like terms.
xb-ax-ab=x^{2}+2x-3-x^{2}
Subtract x^{2} from both sides.
xb-ax-ab=2x-3
Combine x^{2} and -x^{2} to get 0.
-ax-ab=2x-3-xb
Subtract xb from both sides.
\left(-x-b\right)a=2x-3-xb
Combine all terms containing a.
\left(-x-b\right)a=-bx+2x-3
The equation is in standard form.
\frac{\left(-x-b\right)a}{-x-b}=\frac{-bx+2x-3}{-x-b}
Divide both sides by -x-b.
a=\frac{-bx+2x-3}{-x-b}
Dividing by -x-b undoes the multiplication by -x-b.
a=-\frac{-bx+2x-3}{x+b}
Divide 2x-3-xb by -x-b.
x^{2}+xb-ax-ab=\left(x-1\right)\left(x+3\right)
Use the distributive property to multiply x-a by x+b.
x^{2}+xb-ax-ab=x^{2}+2x-3
Use the distributive property to multiply x-1 by x+3 and combine like terms.
xb-ax-ab=x^{2}+2x-3-x^{2}
Subtract x^{2} from both sides.
xb-ax-ab=2x-3
Combine x^{2} and -x^{2} to get 0.
xb-ab=2x-3+ax
Add ax to both sides.
\left(x-a\right)b=2x-3+ax
Combine all terms containing b.
\left(x-a\right)b=ax+2x-3
The equation is in standard form.
\frac{\left(x-a\right)b}{x-a}=\frac{ax+2x-3}{x-a}
Divide both sides by x-a.
b=\frac{ax+2x-3}{x-a}
Dividing by x-a undoes the multiplication by x-a.
Examples
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{ 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}