Question

If $x-\frac{2}{x-1}=1-\frac{2}{x-1}$, then number of solution is:

• A. $1$
• B. $2$
• C. $3$
• D. no solution

Answer 1

The correct option is A $1$

As denominator $\ne 0$

$\Rightarrow x\ne 2$

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

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

$\Rightarrow x^2-2x+1=0$

$\Rightarrow (x-1{)}^2=0$

$\Rightarrow x=1$

$\Rightarrow \left(A\right)$.