Réponse :
(E) (x - 3)/(x - 1) = (x - 5)/(x - 2)
1) (x - 3)/(x - 1) - (x - 5)/(x - 2) = 0 x ≠ 1 et x ≠ 2
⇔ (x - 3)(x - 2)/(x - 1)(x - 2) - (x - 5)(x - 1)/(x - 1)(x - 2) = 0
⇔ (x² - 5 x + 6 - (x² - 6 x + 5))/(x - 1)(x - 2) = 0
⇔ (x² - 5 x + 6 - x² + 6 x - 5)/(x - 1)(x - 2) = 0
⇔ (x + 1)/(x - 1)(x - 2) = 0
⇔ x + 1 = 0
⇔ x = - 1
2) (x - 3)/(x - 1) = (x - 5)/(x - 2) ⇔ (x - 3)(x - 2) = (x - 5)(x - 1)
⇔ x² - 5 x + 6 = x² - 6 x + 5
⇔ x = - 1
Explications étape par étape :
