Réponse :
Explications étape par étape
Bonjour
Résous les équations suivantes :
1) 2x-1=3(x+2)
2x - 1 = 3x + 6
3x - 2x = -6 - 1
x = -7
2) 5(x-4)-3(1-3x)=7
5x - 20 - 3 + 9x = 7
14x = 30
x = 30/14
x = 15/7
3) x/4-x/3=1/6
3x/12 - 4x/12 = 1/6
-x/12 = 1/6
x = 1/6 * -12
x = -2
4) 2x-1/3-x-2/4=0
x = 1/2 + 1/3
x = 3/6 + 2/6
x = 5/6
5) 2x(x-2)=(2x-3)(x+2)
2x^2 - 4x = 2x^2 + 4x - 3x - 6
-5x = -6
x = 6/5
6) 2(x^2 -3)-(2x-1)(x+1)=0
2x^2 - 6 - (2x^2 + 2x - x - 1) = 0
2x^2 - 6 - 2x^2 - x + 1 = 0
x = -5
7) x-1/2=2/3
x = 2/3 + 1/2
x = 4/6 + 3/6
x = 7/6
8) 4/x+3=2/5
4/(x + 3) = 2/5 avec [tex]x + 3\ne0 => x\ne -3[/tex]
4 * 5 = 2(x + 3)
20 = 2x + 6
2x = 20 - 6
x = 14/2
x = 7
9) x-1/x+3=2/3
(x - 1)/(x + 3) = 2/3 (avec [tex]x + 3 \ne 0[/tex])
3(x - 1) = 2(x + 3)
3x - 3 = 2x + 6
3x - 2x = 6 + 3
x = 9
10) x+3/x-2=x-3/x+1
(x + 3)/(x - 2) = (x - 3)/(x + 1)
Avec : [tex]x - 2 \ne 0[/tex]
[tex]x \ne 2[/tex]
Et
[tex]x + 1 \ne 0 => x \ne -1[/tex]
(x + 1)(x + 3) = (x - 3)(x - 2)
x^2 + 3x + x + 3 = x^2 - 2x - 3x + 6
4x + 3 = -5x + 6
4x + 5x = 6 - 3
9x = 3
x = 3/9
x = 1/3
