Question

1÷x-1÷x-2=3
(X not=0,2
​

Answer 1

$Solution$

$= > \frac{1}{x} - \frac{1}{x - 2} = 3 \\ \\ = > \frac{x - 2 - x}{ {x}^{2} - 2x } = 3 \\ \\ = > - 2 = 3 {x}^{2} - 6x \\ \\ = > 3 {x}^{2} - 6x + 2 = 0$

$D = {b}^{2} - 4ac$

$D = { (- 6)}^{2} - 4(3)(2) \\ \\ \: \: \: \: \: = 36 - 24 \\ \\ \: \: \: \: \: = 12 \\ \\ \: \: \: \: \: = 2 \sqrt{3}$

$= > \alpha = \frac{ - b \: + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{6 + 2 \sqrt{3} }{6} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3 + \sqrt{3} }{3}$

$= > \beta = \frac{ - b \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{6 - 2 \sqrt{3} }{6} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3 - \sqrt{3} }{3}$

$Hope\: you \:got\: it$