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