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.