Réponse :
Explications étape par étape
Bonjour
Exercice 96 :
2/(x + 3) = 3/(x + 2)
[tex]x + 3 \ne 0[/tex]
[tex]x \ne -3[/tex]
[tex]x + 2 \ne 0[/tex]
[tex]x \ne -2[/tex]
2(x + 2) = 3(x + 3)
2x + 4 = 3x + 9
4 - 9 = 3x - 2x
-5 = x
x = -5
1/(x - 4) - 1/x = 0
[tex]x - 4 \ne 0[/tex]
[tex]x \ne 4[/tex]
[tex]x \ne 0[/tex]
1/(x - 4) = 1/x
x = x - 4
x - x = -4
0 = -4
Impossible pas de solution
Exercice 97 :
(x + 4)/(x - 2) = 2/3
[tex]x - 2 \ne 0[/tex]
[tex]x \ne 2[/tex]
3(x + 4) = 2(x - 2)
3x + 12 = 2x - 4
3x - 2x = -4 - 12
x = -16
(x+ 2)/(x - 3) = (x - 3)/(x + 2)
[tex]x - 3 \ne 0[/tex]
[tex]x \ne 3[/tex]
[tex]x + 2 \ne 0[/tex]
[tex]x \ne -2[/tex]
(x + 2)^2 = (x - 3)^2
(x + 2)^2 - (x - 3)^2 = 0
(x + 2 - x + 3)(x + 2 + x - 3) = 0
5(2x - 1) = 0
2x - 1 = 0
2x = 1
x = 1/2
