Evaluate
\frac{4\left(2x^{2}+1\right)}{\left(x^{2}-1\right)^{2}}
Expand
\frac{4\left(2x^{2}+1\right)}{\left(x^{2}-1\right)^{2}}
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\frac{2x+1}{\left(x-1\right)^{2}}-\frac{2}{\left(x-1\right)\left(x+1\right)}-\frac{2x-1}{x^{2}+2x+1}
Factor x^{2}-2x+1. Factor x^{2}-1.
\frac{\left(2x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)^{2} and \left(x-1\right)\left(x+1\right) is \left(x+1\right)\left(x-1\right)^{2}. Multiply \frac{2x+1}{\left(x-1\right)^{2}} times \frac{x+1}{x+1}. Multiply \frac{2}{\left(x-1\right)\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{\left(2x+1\right)\left(x+1\right)-2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Since \frac{\left(2x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)^{2}} and \frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+2x+x+1-2x+2}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Do the multiplications in \left(2x+1\right)\left(x+1\right)-2\left(x-1\right).
\frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Combine like terms in 2x^{2}+2x+x+1-2x+2.
\frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{\left(x+1\right)^{2}}
Factor x^{2}+2x+1.
\frac{\left(2x^{2}+x+3\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}}-\frac{\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x-1\right)^{2} and \left(x+1\right)^{2} is \left(x-1\right)^{2}\left(x+1\right)^{2}. Multiply \frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}} times \frac{x+1}{x+1}. Multiply \frac{2x-1}{\left(x+1\right)^{2}} times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.
\frac{\left(2x^{2}+x+3\right)\left(x+1\right)-\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Since \frac{\left(2x^{2}+x+3\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}} and \frac{\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}+2x^{2}+x^{2}+x+3x+3-2x^{3}+4x^{2}-2x+x^{2}-2x+1}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Do the multiplications in \left(2x^{2}+x+3\right)\left(x+1\right)-\left(2x-1\right)\left(x-1\right)^{2}.
\frac{8x^{2}+4}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Combine like terms in 2x^{3}+2x^{2}+x^{2}+x+3x+3-2x^{3}+4x^{2}-2x+x^{2}-2x+1.
\frac{8x^{2}+4}{x^{4}-2x^{2}+1}
Expand \left(x-1\right)^{2}\left(x+1\right)^{2}.
\frac{2x+1}{\left(x-1\right)^{2}}-\frac{2}{\left(x-1\right)\left(x+1\right)}-\frac{2x-1}{x^{2}+2x+1}
Factor x^{2}-2x+1. Factor x^{2}-1.
\frac{\left(2x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)^{2} and \left(x-1\right)\left(x+1\right) is \left(x+1\right)\left(x-1\right)^{2}. Multiply \frac{2x+1}{\left(x-1\right)^{2}} times \frac{x+1}{x+1}. Multiply \frac{2}{\left(x-1\right)\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{\left(2x+1\right)\left(x+1\right)-2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Since \frac{\left(2x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)^{2}} and \frac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+2x+x+1-2x+2}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Do the multiplications in \left(2x+1\right)\left(x+1\right)-2\left(x-1\right).
\frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{x^{2}+2x+1}
Combine like terms in 2x^{2}+2x+x+1-2x+2.
\frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}}-\frac{2x-1}{\left(x+1\right)^{2}}
Factor x^{2}+2x+1.
\frac{\left(2x^{2}+x+3\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}}-\frac{\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x-1\right)^{2} and \left(x+1\right)^{2} is \left(x-1\right)^{2}\left(x+1\right)^{2}. Multiply \frac{2x^{2}+x+3}{\left(x+1\right)\left(x-1\right)^{2}} times \frac{x+1}{x+1}. Multiply \frac{2x-1}{\left(x+1\right)^{2}} times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.
\frac{\left(2x^{2}+x+3\right)\left(x+1\right)-\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Since \frac{\left(2x^{2}+x+3\right)\left(x+1\right)}{\left(x-1\right)^{2}\left(x+1\right)^{2}} and \frac{\left(2x-1\right)\left(x-1\right)^{2}}{\left(x-1\right)^{2}\left(x+1\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{3}+2x^{2}+x^{2}+x+3x+3-2x^{3}+4x^{2}-2x+x^{2}-2x+1}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Do the multiplications in \left(2x^{2}+x+3\right)\left(x+1\right)-\left(2x-1\right)\left(x-1\right)^{2}.
\frac{8x^{2}+4}{\left(x-1\right)^{2}\left(x+1\right)^{2}}
Combine like terms in 2x^{3}+2x^{2}+x^{2}+x+3x+3-2x^{3}+4x^{2}-2x+x^{2}-2x+1.
\frac{8x^{2}+4}{x^{4}-2x^{2}+1}
Expand \left(x-1\right)^{2}\left(x+1\right)^{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}