Question

simplifique (n+4)! /(n+2)! +(n+3)!

Answer 1

$\frac{(n+4)!}{(n+2)!+(n+3)!} = \frac{(n+4)(n+3)(n+2)!}{(n+2)!+(n+3)(n+2)!} = \\ \\ = \frac{(n+4)(n+3)(n+2)!}{(n+2)!(1+n+3)} = \frac{(n+4)(n+3)}{(n+4)}=n+3$