Question

Помогите пожалуйста, надо написать полное решение

Answer 1

$\frac{ {x}^{2} - 4}{ {x}^{2} - 1 } = \frac{(x - 2)(x + 2)}{(x + 1)(x -1 )}$

$\frac{x - 2}{x + 1} = a \\ \frac{x + 2}{x - 1} = b$

$5{a}^{2} - 44 {b}^{2} + 12ab = 0 \\ 5 {a}^{2} - 10ab + 22ab - 44 {b}^{2} = 0 \\ 5a(a - 2b) + 22b(a - 2b) = 0 \\ (a - 2b)(5a + 22b) = 0 \\ a = 2b \\ 5a = - 22b$

$\frac{x - 2}{x + 1} = 2 \times \frac{x + 2}{x - 1} \\ \frac{x - 2}{x + 1} = \frac{2x + 4}{x - 1 } \\ (x - 2)(x - 1) = (2x + 4)(x + 1) \\ {x}^{2} - 3x + 2 = 2 {x}^{2} + 6x + 4 \\ {x}^{2} + 9x + 2 = 0 \\ d = 81 - 8 = 73 \\ x = \frac{ - 9 + - \sqrt{73} }{2}$