\frac{ { x }^{ 2 } +2 }{ x } = { x }^{ } -2
Solve for x
x=-1
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x^{2}+2=xx^{1}+x\left(-2\right)
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.
x^{2}+2=x^{2}+x\left(-2\right)
To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.
x^{2}+2-x^{2}=x\left(-2\right)
Subtract x^{2} from both sides.
2=x\left(-2\right)
Combine x^{2} and -x^{2} to get 0.
x\left(-2\right)=2
Swap sides so that all variable terms are on the left hand side.
x=\frac{2}{-2}
Divide both sides by -2.
x=-1
Divide 2 by -2 to get -1.
Examples
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{ 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}