Question

simplifique : n!-(n+!)!/ (n-1)!+(n-2)! pfvv preciso dos calculos 

Answer 1

$\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=\dfrac{n.(n-1).(n-2)!-(n+1).n.(n-1).(n-2)!}{(n-1).(n-2)!+(n-2)!}$

Colocando (n - 2)! em evidência no numerador e denominador:

$\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=\dfrac{(n-2)!*[n(n-1)-n(n+1)(n-1)]}{(n-2)!*[n-1+1]}$

Cortando (n - 2)!

$\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=\dfrac{n(n-1)-n(n+1)(n-1)}{n}$

Dividindo em cima e embaixo por n:

$\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=(n-1)-(n+1)(n-1)$

Colocando (n - 1) em evidência:

$\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=(n-1)*(1-[n+1])\\\\\\\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=(n-1)*(1-n-1)\\\\\\\boxed{\boxed{\dfrac{n!-(n+1)!}{(n-1)!+(n-2)!}=-n(n-1)}}$