Verified answer

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Verified answer

(x-3)/(x-2) + (x-2)/(x-3) = 2 1/2

ОДЗ x≠2 x≠3

очень много уравнений идет на выражение x + 1/x = 5/2

замена (x-3)/(x-2) = t

t + 1/t = 5/2

(2t² - 5t + 2)/t = 0

D=25 - 16 = 9

t12=(5+-3)/4 = 2   1/2

1/ t=2

(x-3)/(x-2)=2

x-3 = 2x - 4

x = 1

2/ (x-3)/(x-2) = 1/2

2x - 6 = x - 2

x=4

ответ -1 и 4

--------------------

ну можно немного упростить

(x-3)/(x-2) = (x-2 -1)/(x-2) = 1 - 1/(x-2)

(x-2)/(x-3) = (x-3 + 1)/(x-3) = 1 + 1/(x-3)

1/(x-3) - 1/(x-2) = 1/2 и решать уже такое