Prove that : n! (n+2) = n! + (n+1)!

Proof:
n! + (n+1)!=
n! + (n+1)*(n)(n-1)(n-2)...=
n! + (n+1)n!=
n![1+(n+1)]=
n!(n+2)


or...

n!(n+2)=
n![(n+1)+1]=
n!*(n+1)+1*n!=
(n+1)!+n!=
n!+(n+1)!