Evaluate
\frac{x^{2}+6x+1}{\left(x-1\right)\left(x+1\right)^{2}}
Expand
\frac{x^{2}+6x+1}{\left(x-1\right)\left(x^{2}+2x+1\right)}
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\frac{x+1}{x^{2}-1}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Combine 2x and -x to get x.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Factor the expressions that are not already factored in \frac{x+1}{x^{2}-1}.
\frac{1}{x-1}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Cancel out x+1 in both numerator and denominator.
\frac{1}{x-1}+\frac{4x}{\left(x-1\right)\left(x+1\right)^{2}}
Factor \left(x-1\right)\left(x^{2}+2x+1\right).
\frac{\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)^{2}}+\frac{4x}{\left(x-1\right)\left(x+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right)^{2} is \left(x-1\right)\left(x+1\right)^{2}. Multiply \frac{1}{x-1} times \frac{\left(x+1\right)^{2}}{\left(x+1\right)^{2}}.
\frac{\left(x+1\right)^{2}+4x}{\left(x-1\right)\left(x+1\right)^{2}}
Since \frac{\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)^{2}} and \frac{4x}{\left(x-1\right)\left(x+1\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{x^{2}+2x+1+4x}{\left(x-1\right)\left(x+1\right)^{2}}
Do the multiplications in \left(x+1\right)^{2}+4x.
\frac{x^{2}+6x+1}{\left(x-1\right)\left(x+1\right)^{2}}
Combine like terms in x^{2}+2x+1+4x.
\frac{x^{2}+6x+1}{x^{3}+x^{2}-x-1}
Expand \left(x-1\right)\left(x+1\right)^{2}.
\frac{x+1}{x^{2}-1}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Combine 2x and -x to get x.
\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Factor the expressions that are not already factored in \frac{x+1}{x^{2}-1}.
\frac{1}{x-1}+\frac{4x}{\left(x-1\right)\left(x^{2}+2x+1\right)}
Cancel out x+1 in both numerator and denominator.
\frac{1}{x-1}+\frac{4x}{\left(x-1\right)\left(x+1\right)^{2}}
Factor \left(x-1\right)\left(x^{2}+2x+1\right).
\frac{\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)^{2}}+\frac{4x}{\left(x-1\right)\left(x+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right)^{2} is \left(x-1\right)\left(x+1\right)^{2}. Multiply \frac{1}{x-1} times \frac{\left(x+1\right)^{2}}{\left(x+1\right)^{2}}.
\frac{\left(x+1\right)^{2}+4x}{\left(x-1\right)\left(x+1\right)^{2}}
Since \frac{\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)^{2}} and \frac{4x}{\left(x-1\right)\left(x+1\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{x^{2}+2x+1+4x}{\left(x-1\right)\left(x+1\right)^{2}}
Do the multiplications in \left(x+1\right)^{2}+4x.
\frac{x^{2}+6x+1}{\left(x-1\right)\left(x+1\right)^{2}}
Combine like terms in x^{2}+2x+1+4x.
\frac{x^{2}+6x+1}{x^{3}+x^{2}-x-1}
Expand \left(x-1\right)\left(x+1\right)^{2}.
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\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
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