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