Объяснение:
3.(3х + 1)/(х + 2) = 1 + (х - 1)/(х - 2),
(3х + 1)(х - 2)/(х - 2)(х + 2) = (х - 2)(х + 2)/(х - 2)(х + 2) + (х - 1)(х + 2)/(х - 2)(х + 2),
(3х + 1)(х - 2)/(х - 2)(х + 2) - (х - 2)(х + 2)/(х - 2)(х + 2) -
- (х - 1)(х + 2)/(х - 2)(х + 2) = 0,
(3х² - 6х + х - 2 - х² + 4 - х² - 2х + х + 2)/(х - 2)(х + 2) = 0,
(х² - 6х + 4)/(х - 2)(х + 2) = 0,
ОДЗ:
(х - 2)(х + 2) ≠ 0,
х - 2 ≠ 0, х + 2 ≠ 0,
х ≠ 2, х ≠ -2,
х² - 6х + 4 = 0,
Д = (-6)² - 4*1*4 = 36 - 16 = 20, (√20 = √(4*5) = 2√5)
х1 = (6 + 2√5) / 2*1 = 3 + √5,
х2 = (6 - 2√5) / 2*1 = 3 - √5,
5.(х + 9/(х - 6)) : (3х² - 18х + 27)/(х² - 36) =
= (х(х - 6)/(х - 6) + 9/(х - 6)) * (х² - 36)/(3х² - 18х + 27) =
= (х² - 6х + 9)/(х - 6) * (х - 6)(х + 6)/3*(х² - 6х + 9) =
= (х + 6)/3
