(n³+1)/(-1)((n+1)³+1)
You asked:
Evaluate the expression: \(\frac{{n}^{3} + 1}{-1 \cdot \left({\left( n + 1 \right)}^{3} + 1\right)}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{{n}^{3} + 1}{-1 \cdot \left({\left( n + 1 \right)}^{3} + 1\right)} = \frac{n^{3} + 1}{- \left(n + 1\right)^{3} - 1} \)
Expanded
\[\frac{{n}^{3} + 1}{-1 \cdot \left({\left( n + 1 \right)}^{3} + 1\right)} = \frac{n^{3}}{- n^{3} - 3 n^{2} - 3 n - 2} + \frac{1}{- n^{3} - 3 n^{2} - 3 n - 2}\]
Factored
\[\frac{{n}^{3} + 1}{-1 \cdot \left({\left( n + 1 \right)}^{3} + 1\right)} = - \frac{\left(n + 1\right) \left(n^{2} - n + 1\right)}{\left(n + 2\right) \left(n^{2} + n + 1\right)}\]