SOLUTION: simplify fully: n!-2(n-2)!/(n-2)(n-2)! State any restrictions on "n" Thank you!

Question 594527: simplify fully: n!-2(n-2)!/(n-2)(n-2)! State any restrictions on "n"

Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
$\frac{n! - 2(n-2)!}{(n-2)(n-2)!}$

$\frac{n(n-1)(n-2)! - 2(n-2)!}{(n-2)(n-2)!}$

$\frac{(n-2)!(n(n-1) - 2)}{(n-2)(n-2)!}$

$\frac{n(n-1) - 2}{n-2}$

$\frac{n^2 - n - 2}{n-2}$

$\frac{(n-2)(n+1)}{n-2}$

$n+1$

So $\frac{n! - 2(n-2)!}{(n-2)(n-2)!} = n+1 \ \text{for all integer values of n where } n > 2$
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