Question

СРОЧНО 7. Розв’яжіть рівняння: (x-2)/(x^2-x)+ 1/(x^2+x) =2/(x^2-1)

Answer 1

Ответ:

$\frac{x - 2}{ {x}^{2} - x } + \frac{1}{ {x}^{2} + x } = \frac{2}{ {x}^{2} - 1} \\ \frac{x - 2}{x(x - 1)} + \frac{1}{x(x + 1)} - \frac{2}{(x - 1)(x + 1)} = 0 \\ \frac{(x - 2)(x + 1) + x - 1 - 2x}{x(x - 1)(x + 1)} = 0 \\ \frac{ {x}^{2} + x - 2x - 2 - x - 1}{x(x - 1)(x + 1)} = 0 \\ \frac{ {x}^{2} - 2x - 3}{x(x - 1)(x + 1)} = 0 \\ {x}^{2} - 2x - 3 = 0 \\ x \: ne = 0 \: 1 \: - 1 \\ d = {2}^{2} - 4 \times ( - 3) = 16 \\ x1 = \frac{2 - 4}{2} = - 1 \\ x2 = \frac{2 + 4}{2} = 3 \\ x = 3$