# The number of roots of the eqn., $x-\large\frac{2}{x-1}$$=1-\large\frac{2}{x-1} is \begin{array}{1 1}(A) \;1 \\(B)\;2\;imaginary \;solutions \\(C)\;0\;or\;no\;solution \\(D)\;Infinite\;solution \end{array} ## 1 Answer The given equation x-\large\frac{2}{x-1}$$=1-\large\frac{2}{x-1}$ is defined only if $x\neq 1$
Because for $x=1$ the denominator becomes $0$
$\therefore$ for $x\neq 1$ the equation becomes $x=1$
which is contradiction to $x\neq 1$