I have noticed that sometimes, you run into problems where you will get a wrong answer unless you simplify.
If I simply multiply both sides by x^2-1, I get 3x-3=0 or 3x=3 or x=1.
However, the true answer is that there are no roots.
That can be obtained by simplifying:
How come this is so important? How does it change the whole ordeal to simplify without changing the content?