Question

Solve for x :
(ii) $\frac{1}{x}-\frac{1}{x-2}=3,x\ne 0,2$

• A. $\frac{-3\pm \sqrt{3}}{3}$
• B. $\frac{3+\sqrt{3}}{3}$
• C. $\frac{3-\sqrt{3}}{3}$
• D. both b and c

Answer 1

The correct option is D both b and c

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

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

$\Rightarrow$ $\frac{-2}{x^2-2x}=3$

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

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

$\Rightarrow$ Here, $a=3,b=-6,c=2$

$\Rightarrow$ $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-(-6)\pm \sqrt{(-6{)}^2-4(3\left)\right(2)}}{2\left(3\right)}$

$=\frac{6\pm \sqrt{36-24}}{6}$

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

$=\frac{6\pm 2\sqrt{3}}{6}$

$=\frac{3\pm \sqrt{3}}{3}$

$\therefore$ $x=\frac{3+\sqrt{3}}{3}$ and $x=\frac{3-\sqrt{3}}{3}$