Question

The equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ has

• A. no root
• B. one root
• C. two equal roots
• D. infinitely many roots

Answer 1

Answer: (A)

For equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$, the term ' $x-1^{\prime }$ is in the denominator. Hence the solution isn't defined. For $x=1\Rightarrow x\equiv 1$
We have our equation as $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ cancelling the common term on both sides,we get $x=1$.
But for well defined solution $x\equiv 1$. Hence,this equation has no solution.