Explanation

(d)
We have, $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}.$ If $x \neq 1$ multiplying each term by$(x - 1)$, the given equation reduces to $x(x - 1) = (x - 1)or\ (x - 1)^{2} = 0\ or\ x = 1$ which is not possible as considering $x \neq 1$.
Thus, given equation has no roots.