Question

1/x - 1/x-2 =3
solution​

Answer 1

Solution:

$\frac{1}{x} - \frac{1}{x - 2} = 3 \\ \\ \implies \: \frac{x - 2 - x}{x(x - 2)} = 3 \\ \\ \implies \: - 2 = 3x(x - 2) \\ \\ \implies \: 3x {}^{2} - 6x + 2 = 0$

Here,

a=3,b=-6 and c=2.

Discriminant,

D= b^2-4ac

=(-6)^2-4(3)(2)

=36-24

=12

=2√3

$x = \frac{ - b \pm \: \: \sqrt{D} }{2a} = \frac{ - ( - 6) \pm \: 2 \sqrt{3} }{4} = \frac{6 \pm \: 2 \sqrt{3} }{4} = \frac{2(3 \pm \: \sqrt{3)} }{4} = \frac{3 \pm \: \sqrt{3} }{2} = \frac{3 + \sqrt{3} }{2} \: \: or \: \: \frac{3 - \sqrt{3} }{2}$