§ 44: 44.14

44.14 Розв’яжіть нерівність:

1) x-2x+3 ≥ 3x-4x+3;

x-2-3xx+3 ≥ 0; x = 1; x = 3.

x ∈ (–3; 1].

2) x-1x – x+1x-1 < 2; (x-1)2-xx+1-2x(x-1)x(x-1) < 0;

x2-2x+1-x2 -x-2x2+2xx(x-1) < 0; -2x2-x+1x(x-1) < 0 |× (–1);

2x2+x-1x(x-1) > 0; D = 1 + 8 = 9; x₁ = -1+34 = 12; x₂ = –1.

2(x- 12)(x+1)x(x-1) > 0;

x ∈ (–∞; –1) ∪ (0; 12) ∪ (1; +∞).