Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y}{y+1}\text{, }&y\neq -1\\x\in \mathrm{C}\text{, }&y=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y}{y+1}\text{, }&y\neq -1\\x\in \mathrm{R}\text{, }&y=1\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=1\text{, }&\text{unconditionally}\\y=-\frac{x}{x-1}\text{, }&x\neq 1\end{matrix}\right.
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y^{2}x+y-x=y^{2}
Subtract x from both sides.
y^{2}x-x=y^{2}-y
Subtract y from both sides.
\left(y^{2}-1\right)x=y^{2}-y
Combine all terms containing x.
\frac{\left(y^{2}-1\right)x}{y^{2}-1}=\frac{y\left(y-1\right)}{y^{2}-1}
Divide both sides by y^{2}-1.
x=\frac{y\left(y-1\right)}{y^{2}-1}
Dividing by y^{2}-1 undoes the multiplication by y^{2}-1.
x=\frac{y}{y+1}
Divide y\left(-1+y\right) by y^{2}-1.
y^{2}x+y-x=y^{2}
Subtract x from both sides.
y^{2}x-x=y^{2}-y
Subtract y from both sides.
\left(y^{2}-1\right)x=y^{2}-y
Combine all terms containing x.
\frac{\left(y^{2}-1\right)x}{y^{2}-1}=\frac{y\left(y-1\right)}{y^{2}-1}
Divide both sides by y^{2}-1.
x=\frac{y\left(y-1\right)}{y^{2}-1}
Dividing by y^{2}-1 undoes the multiplication by y^{2}-1.
x=\frac{y}{y+1}
Divide y\left(-1+y\right) by y^{2}-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}