résoudre les équations : (3x+2)/3-(x-3)/2=x-1/6 : (x-3)²=(3x-1)²

Bonjour

Résoudre les équations :

2 possibilités soit : (x - 1)/6

(3x+2)/3-(x-3)/2= (x - 1)/6

2(3x + 2)/6 - 3(x - 3)/6 = (x - 1)/6

6x + 4 - 3x + 9 = 6(x - 1)/6

3x + 13 = x - 1

3x - x = -1 - 13

2x = -14

x = -14/2

x = -7

Soit : x - (1/6)

(3x+2)/3-(x-3)/2=x - 1/6

2(3x + 2) - 3(x - 3) = 6(x - 1/6)

6x + 4 - 3x + 9 = 6x - 1

13 + 3x = 6x - 1

13 + 1 = 6x - 3x

14 = 3x

x = 14/3

(x-3)²=(3x-1)²

(x - 3)² - (3x - 1)² = 0

(x - 3 - 3x + 1)(x - 3 + 3x - 1) = 0

(-2x - 2)(4x - 4) = 0

-2(x + 1) * 4(x - 1) = 0

-8(x + 1)(x - 1) = 0

x + 1 = 0 ou x - 1 = 0

x = -1 ou x = 1