Question

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

Answer 1

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

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

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

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

$\Rightarrow x=\frac{6\pm \sqrt{36-4}\left(3\right)\left(2\right)}{2\times 3}$

$x=\frac{6\pm \sqrt{12}}{6}$