Solve for y (complex solution)
\left\{\begin{matrix}y=0\text{, }&x\neq -1\text{ and }x\neq 1\\y\in \mathrm{C}\text{, }&x=-\sqrt{2}\text{ or }x=\sqrt{2}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=0\text{, }&|x|\neq 1\\y\in \mathrm{R}\text{, }&|x|=\sqrt{2}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=-\sqrt{2}\approx -1.414213562\text{; }x=\sqrt{2}\approx 1.414213562\text{, }&\text{unconditionally}\\x\in \mathrm{C}\setminus -1,1\text{, }&y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=\sqrt{2}\approx 1.414213562\text{; }x=-\sqrt{2}\approx -1.414213562\text{, }&\text{unconditionally}\\x\in \mathrm{R}\setminus 1,-1\text{, }&y=0\end{matrix}\right.
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y-\frac{y}{x^{2}-1}=0
Subtract \frac{y}{x^{2}-1} from both sides.
y-\frac{y}{\left(x-1\right)\left(x+1\right)}=0
Factor x^{2}-1.
\frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{y}{\left(x-1\right)\left(x+1\right)}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{y\left(x-1\right)\left(x+1\right)-y}{\left(x-1\right)\left(x+1\right)}=0
Since \frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{y}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}y+yx-yx-y-y}{\left(x-1\right)\left(x+1\right)}=0
Do the multiplications in y\left(x-1\right)\left(x+1\right)-y.
\frac{x^{2}y-2y}{\left(x-1\right)\left(x+1\right)}=0
Combine like terms in x^{2}y+yx-yx-y-y.
x^{2}y-2y=0
Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).
\left(x^{2}-2\right)y=0
Combine all terms containing y.
y=0
Divide 0 by -2+x^{2}.
y-\frac{y}{x^{2}-1}=0
Subtract \frac{y}{x^{2}-1} from both sides.
y-\frac{y}{\left(x-1\right)\left(x+1\right)}=0
Factor x^{2}-1.
\frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{y}{\left(x-1\right)\left(x+1\right)}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{y\left(x-1\right)\left(x+1\right)-y}{\left(x-1\right)\left(x+1\right)}=0
Since \frac{y\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{y}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}y+yx-yx-y-y}{\left(x-1\right)\left(x+1\right)}=0
Do the multiplications in y\left(x-1\right)\left(x+1\right)-y.
\frac{x^{2}y-2y}{\left(x-1\right)\left(x+1\right)}=0
Combine like terms in x^{2}y+yx-yx-y-y.
x^{2}y-2y=0
Multiply both sides of the equation by \left(x-1\right)\left(x+1\right).
\left(x^{2}-2\right)y=0
Combine all terms containing y.
y=0
Divide 0 by -2+x^{2}.
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}