Question

Simplifique as expressões:
A) (n+3)!
_____
(n+2)!

B) x!
______
(x-3)!

Answer 1

n • (n+3) • (n+2)! / (n+2)!

( cancela os iguais)

n • (n+3)

n^2 + 3n

==================

x! / (x-3)!

x • (x-1) • (x-2) • (x-3)!
_______________
(x-3)!

x • (x-1) • (x-2)

x^2 - x • (x-2)

x^3 - 2x^2 - x^2 - 2x

x^3 - 3x^2 - 2x

Answer 2

$a) \frac{(n+3)!}{(n+2)!} = \frac{(n+3)(n+2)!}{(n+2)!} = n + 3 \\ \\ b) \frac{x!}{(x - 3)!} = \frac{x(x-1)(x-2)(x-3)!}{(x-3)!} = x(x-1)(x-2) = (x^{2}-x)(x-2) \\ \\ x^{3}-2x^{2}-x^{2}+2x = x^{3}-3x^{2}+ 2x$

Espero ter ajudado.