((n+1)/(n^2+3n+1))-((n)/(n^2+n-1))
You asked:
Evaluate the expression: \(\frac{n + 1}{{n}^{2} + 3 n + 1} - \frac{n}{{n}^{2} + n - 1}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{n + 1}{{n}^{2} + 3 n + 1} - \frac{n}{{n}^{2} + n - 1} = - \frac{n}{n^{2} + n - 1} + \frac{n + 1}{n^{2} + 3 n + 1} \)
Expanded
\[\frac{n + 1}{{n}^{2} + 3 n + 1} - \frac{n}{{n}^{2} + n - 1} = - \frac{n}{n^{2} + n - 1} + \frac{n}{n^{2} + 3 n + 1} + \frac{1}{n^{2} + 3 n + 1}\]
Factored
\[\frac{n + 1}{{n}^{2} + 3 n + 1} - \frac{n}{{n}^{2} + n - 1} = - \frac{n^{2} + n + 1}{\left(n^{2} + 3 n + 1\right) \left(n^{2} + n - 1\right)}\]