Question

Solve for x : $\frac{1}{x-2}-\frac{2}{x-1}=\frac{6}{x}$

Answer 1

$\frac{1}{x-2}-\frac{2}{x-1}=\frac{6}{x}$

$\frac{(x-1)-2(x-2)}{(x-1)(x-2)}=\frac{6}{x}$

$x(x-1-2x+4)=6(x^2-3x+2)$

$3x-x^2=6x^2-18x+12$

$7x^2-21x+12=0$

Solving the above quadratic equation we get,

$x=\frac{21\pm \sqrt{105}}{4}$