How can i do this exercice (n+1)! /(n+2)! ?

(n+1)! is equal to (n+1)*n*(n-1)*(n-2)...*3*2*1.  Basically, it multiplies together every positive integer that is at most n+1.  This is the definition of the !, or the factorial function.

(n+2)! is equal to (n+2)*(n+1)*n*(n-1)*(n-2)...*3*2*1, using the same definition.  This thus is equal to (n+1)!*(n+2), so we have:

(n+1)!/(n+1)!(n+2), or:

1/(n+2)

This is our final simplification.