Question

(n+2)!+(n+1)(n-1)! / (n+1)(n-1)

Answer 1

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