Answer
The error occurs on the fifth step, where a division by 0 occurred.
Work Step by Step
Given that: $x = 1$, we can subtract "1" from both sides:
$$x -1 = 1- 1$$ $$x -1 = 0$$
Therefore, you can't divide by $(x-1)$ in this case, because it breaks a math rule.
$$\frac{x(x-1)}{x-1} \ne x$$
In this case, that division doesn't have a result.