Question

​Помогите пожалуйста

Answer 1

х ≠ 2

х ≠ - 2

$\frac{x - 1}{x + 2} + \frac{x}{x - 2} = \frac{8}{ {x}^{2} - 4} \\ \frac{x - 1}{x + 2} + \frac{x}{x - 2} - \frac{8}{(x - 2)(x + 2)} = 0 \\ \frac{(x - 1)(x - 2) + x(x + 2) - 8}{(x - 2)(x + 2)} = 0 \\ \frac{ {x}^{2} - 2x - x + 2 + {x}^{2} + 2x - 8}{(x - 2)(x + 2)} = 0 \\ \frac{2 {x}^{2} - x - 6}{(x - 2)(x + 2)} = 0 \\ 2 {x}^{2} - x - 6 = 0 \\ a = 2 \\ b = - 1 \\ c = - 6 \\ D = {b}^{2} - 4ac = ( - 1) {}^{2} - 4 \times 2 \times ( - 6) = \\ = 1 + 48 = 49 \\ x_{1} = \frac{1 + 7}{2 \times 2} = \frac{8}{4} = 2\\ x_{2} = \frac{1 - 7}{2 \times 2} = - \frac{6}{4} = - 1.5$

Первый корень не подходит

Ответ: х = - 1,5