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Number of roots of equation $x-\large\frac{2}{x-1}$$=1-\large\frac{2}{x-1}$ is

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;2&(D)\;infinitely\; many\end{array} $

1 Answer

$x\neq 1$
$\large\frac{x(x-1)-2}{(x-1)}=\frac{(x-1)-2}{(x-1)}$
$\Rightarrow x^2-x-2=x-3$
$\Rightarrow x^2-2x+1=0$
$\Rightarrow (x-1)^2=0$
$\Rightarrow x=1$
But $x=1$ is not possible
Hence given equation have zero roots.
Hence (A) is the correct answer.
answered Apr 14, 2014 by sreemathi.v
 

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