Evaluate
\frac{2\left(2x^{2}+2x+1\right)}{x^{2}-1}
Factor
\frac{2\left(2x^{2}+2x+1\right)}{x^{2}-1}
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\frac{2}{\left(x-1\right)\left(x+1\right)}+\frac{4x}{x-1}
Factor x^{2}-1.
\frac{2}{\left(x-1\right)\left(x+1\right)}+\frac{4x\left(x+1\right)}{\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 \left(x-1\right)\left(x+1\right) and x-1 is \left(x-1\right)\left(x+1\right). Multiply \frac{4x}{x-1} times \frac{x+1}{x+1}.
\frac{2+4x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}
Since \frac{2}{\left(x-1\right)\left(x+1\right)} and \frac{4x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2+4x^{2}+4x}{\left(x-1\right)\left(x+1\right)}
Do the multiplications in 2+4x\left(x+1\right).
\frac{2+4x^{2}+4x}{x^{2}-1}
Expand \left(x-1\right)\left(x+1\right).
Examples
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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