Question

Simplificando a expressão $\frac{n!+(n+1)!}{(n+2)!}$ , obtemos:

Answer 1

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

Cortando os iguais, temos que:
$\frac{1}{(n+2)(n+1)} + \frac{1}{(n+2)}$

Com o MMC:
$\frac{1+ 1(n+1)}{(n+2)(n+1)} = \frac{(n+2)}{(n+2)(n+1)} = \frac{1}{(n+1)}$

Espero ter ajudado!

Answer 2

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