Solve for y (complex solution)
\left\{\begin{matrix}y=0\text{, }&x\neq -\frac{1}{2}\\y\in \mathrm{C}\text{, }&x=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\neq -\frac{1}{2}\text{, }&y=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=0\text{, }&x\neq -\frac{1}{2}\\y\in \mathrm{R}\text{, }&x=1\end{matrix}\right.
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y\left(x-1\right)=0
Multiply both sides of the equation by 2x+1.
yx-y=0
Use the distributive property to multiply y by x-1.
\left(x-1\right)y=0
Combine all terms containing y.
y=0
Divide 0 by x-1.
y\left(x-1\right)=0
Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+1.
yx-y=0
Use the distributive property to multiply y by x-1.
yx=y
Add y to both sides. Anything plus zero gives itself.
\frac{yx}{y}=\frac{y}{y}
Divide both sides by y.
x=\frac{y}{y}
Dividing by y undoes the multiplication by y.
x=1
Divide y by y.
y\left(x-1\right)=0
Multiply both sides of the equation by 2x+1.
yx-y=0
Use the distributive property to multiply y by x-1.
\left(x-1\right)y=0
Combine all terms containing y.
y=0
Divide 0 by x-1.
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}