Розвяжіть нерівність

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

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

(x(x - 3) + 1)*(x - 3) > (1 - 2(x -3))*(x -3)

(x² - 3x + 1)*(x - 3) > (1 - 2x + 6)*(x -3)

(x² - 3x + 1) > (1 - 2x + 6)

x² - 3x + 2x - 6 > 0

x² - x - 6 > 0

D = 1 - 4 (-6) = 25

x = (1 +5)2 = 3

x = (1 - 5)2 = -2

x > -2

Вiдповiдь: (-2;+∞)