Question

Simplifique as frações:
A) 6!/3!
B) 5! . 8! / 4! . 7!
C) n! / (n-1)
D) n! / (n+2)!

Answer 1

a) $\dfrac{6!}{3!}$

Observe que, $6!=6\times5\times4\times3!$, então:

$\dfrac{6!}{3!}=\dfrac{6\times5\times4\times3!}{3!}=6\times5\times4=120$

b) $\dfrac{5!\cdot8!}{4!\cdot7!}$

Note que, $8!=8\times7!$ e $5!=5\times4!$.

Assim, $\dfrac{5!\cdot8!}{4!\cdot7!}=\dfrac{5\times8\times4!\times7!}{4!\cdot7!}=5\times8=40$

c) $\dfrac{n!}{(n-1)!}$

Observe que, $n!=n(n-1)!$.

Deste modo, $\dfrac{n!}{(n-1)!}=\dfrac{n(n-1)!}{(n-1)!}=n$.

d) $\dfrac{n!}{(n+2)!}$

Temos que, $(n+2)!=(n+2)(n+1)n!$.

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