Verified answer

2/(x - 2) - 2/(x + 1) ≤ 3/(x - 2)²

2/(x - 2) - 2/(x + 1) - 3/(x - 2)² ≤ 0

x ≠ -1 x ≠ 2

приводим к общему знаменателю

(2(x + 1)(x - 2) - 2(x - 2)² - 3(x + 1))/(x + 1)(x - 2)² ≤ 0

(2 (x² - 2x + x - 2) - 2(x² - 4x + 4) - 3x - 3)/(x + 1)(x - 2)² ≤ 0

( 2x² - 2x - 4 - 2x² + 8x - 8 - 3x - 3)/(x + 1)(x - 2)² ≤ 0

(3x - 15)/(x + 1)(x - 2)² ≤ 0

3(x - 5)/(x + 1)(x - 2)² ≤ 0

метод интервалов

++++++++(-1) ------------(2) ----------- [5] +++++++++

x∈ (-1, 2) U (2, 5]

0 1 3 4 5 итого 5 чисел