(x+1/x-2)+(x+2/x-1)-2=0

Question

(x+1/x-2)+(x+2/x-1)-2=0

Answer 1

(x + 1)/(x - 2) + (x + 2)/(x - 1) - 2 = 0

ОДЗ:
x - 2 ≠ 0 ⇒ x ≠ 2
x - 1 ≠ 0 ⇒ x ≠ 1

(x + 1)/(x - 2) + (x + 2)/(x - 1) = 2

Умножаем всё уравнение на (x - 2)(x - 1):

(x + 1)(x - 1) + (x + 2)(x - 2) = 2(x - 1)(x - 2)

x² - 1 + x² - 4 = 2(x² - 2x - x + 2)

2x² - 5 = 2x² - 6x + 4

-5 = -6x + 4

-5 - 4 = -6x

-6x = -9

x = 9:6

x = 1,5 - уд. ОДЗ 

Ответ: x = 1,5.