Evaluate
\frac{x}{x^{2}-1}
Expand
\frac{x}{x^{2}-1}
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\frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}}x
Factor the expressions that are not already factored in \frac{x^{2}-1}{x^{4}-2x^{2}+1}.
\frac{1}{\left(x-1\right)\left(x+1\right)}x
Cancel out \left(x-1\right)\left(x+1\right) in both numerator and denominator.
\frac{x}{\left(x-1\right)\left(x+1\right)}
Express \frac{1}{\left(x-1\right)\left(x+1\right)}x as a single fraction.
\frac{x}{x^{2}-1}
Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
\frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}}x
Factor the expressions that are not already factored in \frac{x^{2}-1}{x^{4}-2x^{2}+1}.
\frac{1}{\left(x-1\right)\left(x+1\right)}x
Cancel out \left(x-1\right)\left(x+1\right) in both numerator and denominator.
\frac{x}{\left(x-1\right)\left(x+1\right)}
Express \frac{1}{\left(x-1\right)\left(x+1\right)}x as a single fraction.
\frac{x}{x^{2}-1}
Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}