Question

How many roots the equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ have

• A. One
• B. Two
• C. Infinite
• D. None

Answer 1

The correct option is D None

If $x\ne 1$, multiplying each term by $(x-1)$,
the given equation reduces to $x(x-1)=(x-1)$
$or(x-1{)}^2=0orx=1,$
Which is not possible as considering $x\ne 1$.
Thus, given equation has no root.