Неравенство: x/(x^2+6x+8)>x/(x^2+7x+10)

   1. Найдем корни трехчленов:

   a) f(x) = x^2 + 6x + 8;

• D/4 = 3^2 - 8 = 1;
• x = -3 ± 1;
• x1 = -4; x2 = -2;
• f(x) = (x + 4)(x + 2).

   b) g(x) = x^2 + 7x + 10;

• D = 7^2 - 4 * 10 = 9;
• x = (-7 ± 3)/2;
• x1 = -5; x2 = -2;
• g(x) = (x + 5)(x + 2).

   2. Решим неравенство:

• x/(x^2 + 6x + 8) > x/(x^2 + 7x + 10);
• x/(x + 4)(x + 2) - x/(x + 5)(x + 2) > 0;
• x/(x + 2)(1/(x + 4) - 1/(x + 5)) > 0;
• x/(x + 2)((x + 5 - x - 4)/(x + 4)(x + 5)) > 0;
• x/(x + 2)(1/(x + 4)(x + 5)) > 0;
• x/((x + 2)(x + 4)(x + 5)) > 0;
• x ∈ (-∞; -5) ∪ (-4; -2) ∪ (0; ∞).

   Ответ: (-∞; -5) ∪ (-4; -2) ∪ (0; ∞).