I have an algebra problem in which I should find $x$. However, even though I manage to define $x = 1$, the text book says that there is no answer. Where am I going wrong in solving it?
$\frac{\frac{x+1}{x-1}-1}{1+\frac{1}{x-1}} = 2$ $\iff \frac{x+1 - (x-1)}{(x-1)+1} = 2$ $\iff \frac{x+1 - x+1}{x-1+1} = 2$ $\iff \frac{2}{x} = 2$ $\iff 2 = 2x \iff x = 1$