options: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
problem_activity: Task
Megan is working solving the equation $$\frac{2}{x^2-1} - \frac{1}{x-1} = \frac{1}{x+1}.$$ She says
If I clear the denominators I find that the only solution is $x = 1$ but when I substitute in $x = 1$ the equation does not make any sense.
Is Megan's work correct?
Why does Megan's method produce an $x$ value that does not solve the equation?


correct_option_index: 1