Question

Find the roots of 1/x -1/x-2 =3,

Answer 1

Answer:

$\frac{1}{x} - \frac{1}{x - 2} = 3 \\ \\ \frac{x - 2 - x}{x(x - 2)} = 3 \\ \\ x(x - 2) = - \frac{2}{3} \\ \\ {x}^{2} - 2x = - \frac{2}{3} \\ \\ 3 {x}^{2} - 6x + 2 = 0 \\ \\ x = \frac{6 + \sqrt{36 - 24} }{6} = \frac{6 + \sqrt{12} }{6} = 1 + \frac{1}{ \sqrt{3} } \\ x = 1 - \frac{1}{ \sqrt{3} }$