I'm probably missing something due to the long day of going through basic materials and practicing a lot, but I'm puzzled.
$e^x(x^2 - 1) = 0$
Now, I could solve this as follows: $e^xx^2 - e^x = 0 \\ e^xx^2 = e^x \\ x^2 = 1 \\ x = \pm1$
Another way could be to divide both sides by $e^x$, giving $x^2 - 1 = 0$, so: $x^2 = 1$ and $x = \pm 1$
But I could've also choosen to divide bot sides by $x^2- 1$, yielding $e^x = 0$, which has no solution...
What am I doing wrong in this last part?