standard_description: 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?


aligns: yes