-1 <= (x^2 - 5x + 4) / (x^2 - 4) <= 1;
(x^2 - 5x + 4) / (x^2 - 4<span>) - 1 <= 0;
</span>(-5x + 8) / ((x - 2) * (x + 2)) <= 0;
x ∈ (-2; -1.6] U (2; +00);
-1 <= (x^2 - 5x + 4) / (x^2 - 4<span>);
</span>(x^2 - 5x + 4) / (x^2 - 4<span>) + 1 >= 0;
</span>(2x^2 - 5x) / ((x - 2) * (x + 2)<span>) >= 0;
</span>x(2x - 5) / ((x - 2) * (x + 2)<span>) >= 0;
</span><span>x ∈ (-00; -2) U [0; 2) U [2.5; +00);
</span>Ответ: <span>x ∈ [2.5; +00).</span>
Y' = 5 - (1/x) = 0
(5x - 1) / x = 0,
5x - 1 = 0, x = 1/5
Если 1/10 <= x <= 1/5, y' < 0
Если 1/5< x <= 1/2, y' > 0
Значит точка x = 1/5 - минимум
y(1/5) = 1 - ln(1) + 12 = 1 - 0 + 12 = 13
Наименьшее значение на промежутке у=13