Question

(n+2)!+(n+1)!
_________
(n+1)!

SIMPLIFIQUE A FRAÇAO

Answer 1

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


Colocando o fator comum $(n+1)!$ em evidência no numerador, e simplificando $(n+1)!$ no numerador e no denominador:

$=\dfrac{(n+1)!\cdot \left[(n+2)+1 \right ]}{(n+1)!}\\ \\ \\ =n+2+1\\ \\ =n+3$

Answer 2

(n+2)!+(n+1)!
-----------------
(n+1)!
=
(n+2)(n+1)! +(n+1)!
-------------------------
(n+1)!
=
=(n+2)+1
=n+3