Step (7) is an error because we are dividing by $x-2$, even though $x-2$ is equal to 0.
Work Step by Step
In step (7) it shows both sides of the equation being divided by $x-2$. This is not allowed, because we know that $x=2$ from step (1), which means that $x-2$ is equal to 0. Dividing numbers by 0 is not allowed.