Question

Помогите пожалуйста решить уравнение.

Answer 1

Ответ:

$\frac{x}{x + 2} + \frac{x + 3}{x - 2} = \frac{8}{ {x}^{2} - 4} \\ \frac{x(x - 2) + (x + 2)(x + 3) - 8}{(x - 2)(x + 2)} = 0 \\ \frac{ {x}^{2} - 2x + {x}^{2} + 3x + 2x + 6 - 8 }{(x - 2)(x + 2)} = 0 \\ \frac{2 {x}^{2} + 4x - x - 2 }{(x - 2)(x + 2)} = 0 \\ \frac{2x(x + 2) - (x + 2)}{(x - 2)(x + 2)} = 0 \\ \frac{(x + 2)(2x - 1)}{(x - 2)(x + 2)} = 0 \\ \frac{2x - 1}{x - 2} = 0 \\ 2x - 1 = 0 \\ 2x = 1 \\ x = \frac{1}{2} \\ x = 0.5$