Pouvez m’aider pur ma 96 et 97 svp

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