Question

Find the roots of the equations :
$\frac{1}{x}-\frac{1}{x-2}=3,x\ne 0,2$

Answer 1

$\frac{1}{x}-\frac{1}{x-2}=3$

$\Rightarrow \frac{x-2-x}{x(x-2)}=3$

$\Rightarrow -2=3x(x-2)$

$\Rightarrow 3x^2-6x+2=0$

$\Rightarrow x=\frac{6\pm \sqrt{36-24}}{6}=\frac{6\pm \sqrt{12}}{6}=\frac{6\pm 2\sqrt{3}}{6}\Rightarrow x=\frac{3\pm \sqrt{3}}{3}$