Solve for x (complex solution)
x=-\frac{2a}{1-a}
a\neq -1\text{ and }a\neq 1
Solve for a
a=-\frac{x}{2-x}
x\neq 2\text{ and }x\neq 1
Solve for x
x=-\frac{2a}{1-a}
|a|\neq 1
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x+a=a\left(x-1\right)
Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.
x+a=ax-a
Use the distributive property to multiply a by x-1.
x+a-ax=-a
Subtract ax from both sides.
x-ax=-a-a
Subtract a from both sides.
x-ax=-2a
Combine -a and -a to get -2a.
\left(1-a\right)x=-2a
Combine all terms containing x.
\frac{\left(1-a\right)x}{1-a}=-\frac{2a}{1-a}
Divide both sides by 1-a.
x=-\frac{2a}{1-a}
Dividing by 1-a undoes the multiplication by 1-a.
x=-\frac{2a}{1-a}\text{, }x\neq 1
Variable x cannot be equal to 1.
x+a=a\left(x-1\right)
Multiply both sides of the equation by x-1.
x+a=ax-a
Use the distributive property to multiply a by x-1.
x+a-ax=-a
Subtract ax from both sides.
x+a-ax+a=0
Add a to both sides.
x+2a-ax=0
Combine a and a to get 2a.
2a-ax=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(2-x\right)a=-x
Combine all terms containing a.
\frac{\left(2-x\right)a}{2-x}=-\frac{x}{2-x}
Divide both sides by -x+2.
a=-\frac{x}{2-x}
Dividing by -x+2 undoes the multiplication by -x+2.
x+a=a\left(x-1\right)
Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.
x+a=ax-a
Use the distributive property to multiply a by x-1.
x+a-ax=-a
Subtract ax from both sides.
x-ax=-a-a
Subtract a from both sides.
x-ax=-2a
Combine -a and -a to get -2a.
\left(1-a\right)x=-2a
Combine all terms containing x.
\frac{\left(1-a\right)x}{1-a}=-\frac{2a}{1-a}
Divide both sides by 1-a.
x=-\frac{2a}{1-a}
Dividing by 1-a undoes the multiplication by 1-a.
x=-\frac{2a}{1-a}\text{, }x\neq 1
Variable x cannot be equal to 1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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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}