Multiple choice

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

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

  2. Both A and R are true and R is not the correct explanation of A.

  3. A is true but R is false.

  4. A is false but R is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation x - 2/(x-1) = 1 - 2/(x-1) simplifies to x = 1. However, the original equation is undefined at x = 1 because of the denominator (x-1). Thus, there is no root. Both statements are correct and logically linked.

AI explanation

For the equation x - 2/(x-1) = 1 - 2/(x-1) to be defined, the denominator cannot be zero, so x - 1 != 0 which means x != 1. By adding 2/(x-1) to both sides, the equation simplifies to x = 1. Since x = 1 is excluded from the domain, the equation has no root, making Reason (R) the correct explanation for Assertion (A).

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