5. Решить уравнение (x - 1)(x + 2) – x(x + 2) = 2x – 1 [x(x + 2) – (x + 3)(x + 1) = 2x + 3].

5. Решить уравнение

$$(x - 1)(x + 2) – x(x + 2) = 2x – 1$$

$$x^2 + 2x - x - 2 - x^2 - 2x = 2x - 1$$

$$x^2 - x^2 + 2x - x - 2x - 2 = 2x - 1$$

$$-x - 2 = 2x - 1$$

$$2x + x = -2 + 1$$

$$3x = -1$$

$$x = -\frac{1}{3}$$

Ответ: $$x = -\frac{1}{3}$$

[x(x + 2) – (x + 3)(x + 1) = 2x + 3].

$$x^2 + 2x - (x^2 + x + 3x + 3) = 2x + 3$$

$$x^2 + 2x - x^2 - 4x - 3 = 2x + 3$$

$$x^2 - x^2 + 2x - 4x - 2x = 3 + 3$$

$$-4x = 6$$

$$x = -\frac{6}{4} = -\frac{3}{2}$$

Ответ: $$x = -\frac{3}{2}$$