Question

Solve the equation $\frac{2}{2-x}+\frac{1}{2}-\frac{4}{x(2-x)}=0$

Answer 1

$\frac{2}{2-x}+\frac{1}{2}-\frac{4}{x(2-x)}=0$

Firstly, for given equation to be valid, $x\ne 0,2$

Now simplifying, we get

$\frac{2}{2-x}+\frac{1}{2}-2\times \frac{2}{x(2-x)}=0$

$\Rightarrow \frac{2}{2-x}+\frac{1}{2}-2\times \frac{x+(2-x)}{x(2-x)}=0$

$\Rightarrow \frac{2}{2-x}+\frac{1}{2}-2\times (\frac{1}{2-x}+\frac{1}{x})=0$

$\Rightarrow \frac{2}{2-x}+\frac{1}{2}-\frac{2}{2-x}-\frac{2}{x}=0$

$\Rightarrow \frac{2}{x}=\frac{1}{2}\Rightarrow x=4$