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\frac{x}{2}
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\frac{x}{2}
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\frac{x+\frac{x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Factor x^{2}-1.
\frac{\frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\frac{x\left(x-1\right)\left(x+1\right)+x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Since \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{3}+x^{2}-x^{2}-x+x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Do the multiplications in x\left(x-1\right)\left(x+1\right)+x.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Combine like terms in x^{3}+x^{2}-x^{2}-x+x.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2\left(x-1\right)}{x-1}+\frac{1}{x-1}-\frac{1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-1}{x-1}.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2\left(x-1\right)+1}{x-1}-\frac{1}{x+1}}
Since \frac{2\left(x-1\right)}{x-1} and \frac{1}{x-1} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x-2+1}{x-1}-\frac{1}{x+1}}
Do the multiplications in 2\left(x-1\right)+1.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x-1}{x-1}-\frac{1}{x+1}}
Combine like terms in 2x-2+1.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{\left(2x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{\left(x-1\right)\left(x+1\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+1 is \left(x-1\right)\left(x+1\right). Multiply \frac{2x-1}{x-1} times \frac{x+1}{x+1}. Multiply \frac{1}{x+1} times \frac{x-1}{x-1}.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{\left(2x-1\right)\left(x+1\right)-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}}
Since \frac{\left(2x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x-1}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x^{2}+2x-x-1-x+1}{\left(x-1\right)\left(x+1\right)}}
Do the multiplications in \left(2x-1\right)\left(x+1\right)-\left(x-1\right).
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x^{2}}{\left(x-1\right)\left(x+1\right)}}
Combine like terms in 2x^{2}+2x-x-1-x+1.
\frac{x^{3}\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\times 2x^{2}}
Divide \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} by \frac{2x^{2}}{\left(x-1\right)\left(x+1\right)} by multiplying \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} by the reciprocal of \frac{2x^{2}}{\left(x-1\right)\left(x+1\right)}.
\frac{x}{2}
Cancel out \left(x-1\right)\left(x+1\right)x^{2} in both numerator and denominator.
\frac{x+\frac{x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Factor x^{2}-1.
\frac{\frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{\frac{x\left(x-1\right)\left(x+1\right)+x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Since \frac{x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{3}+x^{2}-x^{2}-x+x}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Do the multiplications in x\left(x-1\right)\left(x+1\right)+x.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{2+\frac{1}{x-1}-\frac{1}{x+1}}
Combine like terms in x^{3}+x^{2}-x^{2}-x+x.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2\left(x-1\right)}{x-1}+\frac{1}{x-1}-\frac{1}{x+1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-1}{x-1}.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2\left(x-1\right)+1}{x-1}-\frac{1}{x+1}}
Since \frac{2\left(x-1\right)}{x-1} and \frac{1}{x-1} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x-2+1}{x-1}-\frac{1}{x+1}}
Do the multiplications in 2\left(x-1\right)+1.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x-1}{x-1}-\frac{1}{x+1}}
Combine like terms in 2x-2+1.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{\left(2x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{\left(x-1\right)\left(x+1\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+1 is \left(x-1\right)\left(x+1\right). Multiply \frac{2x-1}{x-1} times \frac{x+1}{x+1}. Multiply \frac{1}{x+1} times \frac{x-1}{x-1}.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{\left(2x-1\right)\left(x+1\right)-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}}
Since \frac{\left(2x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{x-1}{\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x^{2}+2x-x-1-x+1}{\left(x-1\right)\left(x+1\right)}}
Do the multiplications in \left(2x-1\right)\left(x+1\right)-\left(x-1\right).
\frac{\frac{x^{3}}{\left(x-1\right)\left(x+1\right)}}{\frac{2x^{2}}{\left(x-1\right)\left(x+1\right)}}
Combine like terms in 2x^{2}+2x-x-1-x+1.
\frac{x^{3}\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\times 2x^{2}}
Divide \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} by \frac{2x^{2}}{\left(x-1\right)\left(x+1\right)} by multiplying \frac{x^{3}}{\left(x-1\right)\left(x+1\right)} by the reciprocal of \frac{2x^{2}}{\left(x-1\right)\left(x+1\right)}.
\frac{x}{2}
Cancel out \left(x-1\right)\left(x+1\right)x^{2} in both numerator and denominator.
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}