1) 16 дробьx (x+1) + 6 дробьx (x-1) = 1 дробьx 2) √3 дробь (х-4) = 2 3) (х+3) (2 х-6) (3 х+4) ≥ 0 4) 3 дробьх+1≤5 дробьх+2 25 х^2-3 ах+1=0

1) 16 / (x + 1) + 6 / (x * (x - 1)) = 1;

16 / (x + 1) * x * (x + 1) * (x - 1) + 6 / (x * (x - 1)) * x * (x + 1) * (x - 1) = 1 * x * (x + 1) * (x - 1);

16 * x * (x - 1) + 6 * (x + 1) = x * (x ^ 2 - 1);

16 * x ^ 2 - 16 + 6 * x + 6 = x ^ 3 - x;

x ^ 3 - x - 16 * x ^ 2 + 16 - 6 * x - 6 = 0;

x ^ 3 - 16 * x ^ 2 - 6 * x + 10 = 0;

x₁ = - 0.965;

x₂ = 16.33;

x₃ = 0.635.

2) √3 / (х - 4) = 2;

2 * (x - 4) = √3;

2 * x - 8 = √3;

2 * x = 8 + √3;

x = (8 + √3) / 2;

3) (х + 3) * (2 * х - 6) * (3 * х + 4) ≥ 0;

{ x + 3 = 0;

2 * x - 6 = 0;

3 * x + 4 = 0;

{ x = - 3;

2 * x = 6;

3 * x = - 4;

{ x = - 3;

x = 3;

x = - 4/3;

Тогда:

- + - +;

_ - 3 _ - 4/3 _ 3 _;

Отсюда, - 3 < = x = 3.

4) 3 / (х + 1) ≤ 5 / (х + 2);

3 * (x + 2) < = 5 * (x + 1);

3 * x + 6 < = 5 * x + 5;

3 * x - 5 * x < = 5 - 6;

- 2 * x < = - 1;

x > = 1/2;

4) 25 * х ^ 2 - 3 * х + 1 = 0;

Найдем дискриминант квадратного уравнения:

D = b ² - 4 * a * c = ( - 3) ² - 4 * 25 * 1 = 9 - 100 = - 91;

Нет корней.