3 (x-1/x+3) ^2-5 (x-1/x+3) = -2

Решим уравнение 3 * ((x - 1) / (x + 3)) ^2 - 5 * ((x - 1) / (x + 3)) = - 2;

3 * ((x - 1) / (x + 3)) ^2 - 5 * ((x - 1) / (x + 3)) + 2 = 0;

Пусть (x - 1) / (x + 3) = t, тогда:

3 * t^2 - 5 * t + 2 = 0;

D = b^2 - 4 * a * c = (-5) ^2 - 4 * 3 * 2 = 25 - 24 = 1;

Найдем корни уравнения.

t1 = ( - (-5) + 1) / (2 * 3) = (5 + 1) / 6 = 6/6 = 1;

t2 = ( - (-5) - 1) / (2 * 3) = (5 - 1) / 6 = 4/6 = 2/3;

1) (x - 1) / (x + 3) = 1;

x - 1 = x + 3;

x - x = 3 + 1;

0 * x = 4;

Нет корней.

2) (x - 1) / (x + 3) = 2/3;

2 * (x + 3) = 3 * (x - 1);

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

2 * x - 3 * x = - 3 - 6;

-x = - 9;

x = 9;

Ответ: х = 9.