Mostrar a forma mais simples da equação dada

[dressa_mwar1]

\(\frac{(n + 2)! + (n + 1)(n - 1)!}{(n + 1)(n - 1)!}\)

[acacio]

n+3

[haroflow]

Olá, segue minha resposta:

\(\begin{align*}
\frac{(n+2)!+(n+1)(n-1)!}{(n+1)(n-1)!} &= \frac{(n+2)!}{(n+1)(n-1)!} + \frac{(n+1)(n-1)!}{(n+1)(n-1)!} \\
&= \frac{(n+2)!}{(n+1)(n-1)!} + 1 \\
&= \frac{(n+2)(n+1)(n)(n-1)!}{(n+1)(n-1)!} + 1 \\
&= \frac{(n+1)(n-1)!((n+2)(n))}{(n+1)(n-1)!} + 1 \\
&= (n+2)(n) + 1 \\
&= n(n+2) + 1 \\
&= n^2+2n + 1
\end{align*}\)

Abraços!