Question

Alguém?

1/x=3/2-1/x-1

Answer 1

1/x = 3/2 - 1/x - 1
1/x + 1/x - 1 = 3/2
m.m.c =  x   x - 1 
1( x - 1 ) + 1 x        3
--------------------  = -------- multiplicando em cruz
x   (x - 1)                2       

2 (x -1) + 2 x  =  3 x (x - 1)
2 x - 2 + 2 x = 3 x² - 3 x
3 x² - 3 x = 2 x - 2 + 2 x
3 x² - 3 x = 4 x - 2
3 x² - 3 x - 4 x + 2 = 0
3 x² - 7 x + 2 = 0
Δ = b² - 4 a. c
Δ = (-7)² - 4 .3 . 2
Δ = 49  - 24
Δ = 25
\/¨¨25 = 5
x = - b +ou- 5/ 2 . 3
x = - (-7) +ou- 5 /6
x´= 7 + 5 /6
x´= 12/6
x´= 2
x" = 7 - 5 /6
x" = 2/6
x" = 1/3

S = {1/3,2}