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