Объяснение:
(x + 1)/(x - 2)-(x + 3)/(x - 1)=1
(x + 1)/(x - 2)-(x + 3)/(x - 1) - 1 = 0
х² - 1 - (х² + 3х - 2х - 6)-(х² - х - 2х + 2) /(х - 2)(х - 1) = 0
х² - 1 - х² - х + 6 - х² + 3х - 2/(х - 2)(х - 1) = 0
3 + 2х - х²/(х - 2)(х - 1) = 0
3 + 2х - х² = 0
х² - 2х - 3 = 0
х(х + 1) - 3(х + 1) = 0
(х + 1)(х - 3) = 0
х + 1 = 0 х - 3 = 0
х = -1 х = 3
ответ : х₁ = - 1 ; х₂ = 3
Объяснение:
(x + 1)/(x - 2)-(x + 3)/(x - 1)=1
(x + 1)/(x - 2)-(x + 3)/(x - 1) - 1 = 0
х² - 1 - (х² + 3х - 2х - 6)-(х² - х - 2х + 2) /(х - 2)(х - 1) = 0
х² - 1 - х² - х + 6 - х² + 3х - 2/(х - 2)(х - 1) = 0
3 + 2х - х²/(х - 2)(х - 1) = 0
3 + 2х - х² = 0
х² - 2х - 3 = 0
х(х + 1) - 3(х + 1) = 0
(х + 1)(х - 3) = 0
х + 1 = 0 х - 3 = 0
х = -1 х = 3
ответ : х₁ = - 1 ; х₂ = 3