Question

The equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ has

• A. no root
• B. one root
• C. two equal roots
• D. infinite roots

Answer 1

The correct option is A no root

consider, $x-\frac{2}{x-1}=1-\frac{2}{x-1}$

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

$\Rightarrow x-1=0$

$\Rightarrow x=1$.

However, as $x\to 1$,

$\left(\frac{2}{x-1}\right)\to \infty$

Hence, the above equation has no root.