Question

Assertion (A): The equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ has no root.
Reason (R): $x-1\ne 0$, then only above equation is defined.

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true and R is not the correct explanation of A.
• C. A is true but R is false.
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A.

$x-\frac{2}{x-1}=1-\frac{2}{x-1}$
$x=1-\frac{2}{x-1}+\frac{2}{x-1}$
$x=1$
However at $x=1$ the expression $\frac{2}{x-1}$ is not defined.
Hence the above equation has no real roots.