Evaluate
\frac{3x+1}{2\left(x^{2}-1\right)}
Expand
\frac{3x+1}{2\left(x^{2}-1\right)}
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\frac{2\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}+\frac{x-1}{2\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 2\left(x+1\right) is 2\left(x-1\right)\left(x+1\right). Multiply \frac{1}{x-1} times \frac{2\left(x+1\right)}{2\left(x+1\right)}. Multiply \frac{1}{2\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{2\left(x+1\right)+x-1}{2\left(x-1\right)\left(x+1\right)}
Since \frac{2\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)} and \frac{x-1}{2\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x+2+x-1}{2\left(x-1\right)\left(x+1\right)}
Do the multiplications in 2\left(x+1\right)+x-1.
\frac{3x+1}{2\left(x-1\right)\left(x+1\right)}
Combine like terms in 2x+2+x-1.
\frac{3x+1}{2x^{2}-2}
Expand 2\left(x-1\right)\left(x+1\right).
\frac{2\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}+\frac{x-1}{2\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 2\left(x+1\right) is 2\left(x-1\right)\left(x+1\right). Multiply \frac{1}{x-1} times \frac{2\left(x+1\right)}{2\left(x+1\right)}. Multiply \frac{1}{2\left(x+1\right)} times \frac{x-1}{x-1}.
\frac{2\left(x+1\right)+x-1}{2\left(x-1\right)\left(x+1\right)}
Since \frac{2\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)} and \frac{x-1}{2\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x+2+x-1}{2\left(x-1\right)\left(x+1\right)}
Do the multiplications in 2\left(x+1\right)+x-1.
\frac{3x+1}{2\left(x-1\right)\left(x+1\right)}
Combine like terms in 2x+2+x-1.
\frac{3x+1}{2x^{2}-2}
Expand 2\left(x-1\right)\left(x+1\right).
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Simultaneous equation
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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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