Question

Simplifique a expressão m! + (m-1)!/(m+1)!-m! =5/16

Answer 1

Explicação passo-a-passo:

m! + (m-1)!

_________= 5/16

(m+1)! - m!

m.(m-1)! + (m-1)!

_________________= 5/16

(m+1).m.(m-1)! - m.(m-1)!

(m-1)! . [ m + 1]

________________= 5/16

(m-1)! [ m.(m+1) - m]

m +1

______________= 5/16

m² + m - m

m+1

___________=5/16

m²

5.m² = 16.(m+1)

5m²= 16m + 16

5m² - 16m - 16=0

∆= (-16)² -4.5.(-16)

∆= 256 + 320

∆= 576

m= - (-16) +√576

___________

2 .5

m = 16 + 24

_______

10

m= 40/10

m= 4

S = { 4}