Simplify:

Question

n!-(n-1)!
---------
(n-1)!

Answer 1

( n(n-1)! - (n-1)! )/(n-1)!
= (n-1)! (n-1)/(n-1)!
=n-1

e.g. (5! - 4!)/4! , for the case n=5
= (5(4!) - 4!)/4!
=4!(5-1)/4!
= 5-1
= 4