Multiple choice

The number of roots of the equation $x-\cfrac { 2 }{ x-1 } =1-\dfrac { 2 }{ x-1 } $ is :

  1. 0

  2. 1

  3. 2

  4. 3
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A Correct answer
Explanation

The equation is x - 2/(x-1) = 1 - 2/(x-1). Adding 2/(x-1) to both sides gives x = 1. However, if x = 1, the term 2/(x-1) is undefined (division by zero). Therefore, there are no valid roots.

AI explanation

By canceling the term -2/(x - 1) from both sides, the equation reduces to x = 1. However, substituting x = 1 into the original equation makes the denominators zero, rendering the expressions undefined. Therefore, the potential root is extraneous, and the equation has 0 valid roots.

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