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  4. The equation x-(2/x-1)=1-(2/x-1) has

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

IIT JEEIIT JEE 1984Complex Numbers and Quadratic Equations

Solution:

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.