везде применяем метод интервалов
1.
(x+2)(x-3)(x-4) < 0
------------ (-2) +++++++++ (3) ------------- (4) ++++++++++
x∈(-∞ -2) U (3 4)
2
(x+5)/(x-2)/(x-1)^2 >=0
++++++++++ [-5] ------------ (1) ------------ [2] +++++++++++
x∈(-∞ -5] U [2 +∞)
3
(2x+1)/(x-3) <=1</p>
(2x+1)/(x-3) - 1<=0</p>
(2x+1 - x + 3)/(x-3)<=0</p>
(x+4)/(x-3)<=0</p>
+++++++ [-4] ------------- (3) +++++++
x∈[-4 3)
4
x/(x-4) + 5/(x-1) + 24/(x-1)(x-4) <=0</p>
(x(x-1) + 5(x-4) + 24)/(x-1)(x-4) <=0</p>
(x^2 - x + 5x - 20 + 24) /(x-1)(x-4) <=0</p>
(x^2-4x+4)/(x-1)(x-4) <=0</p>
(x-2)^2/(x-1)(x-4) <=0</p>
++++++++ (1) -----------[2] ---------- (4) ++++++++
x∈(1 4)