Every step up to and including
seems fine. However, you can't simply divide by
much like how you can't divide both sides of
by
. Doing so is equivalent to dividing by 0, as
is a solution. The correct way to solve it would be to subtract
from both sides, which leaves the solution
. Thus, the only way for a solution to exist is if
(i.e. to include 0 in the domain).
In regards to why this is the case, I'm still trying to get my head around it. One would think that the derivative of both sides would be the same for all
since
. However, this definition would start to get a bit iffy for non-integer values of
. But then that just raises another question: why would this only be true for
, and not all integer
values? Regardless, you can't get
since the step you took (i.e. dividing by 0) would result in the end of the universe as we know it.
@Drdusk I'm also thinking about your point of having
terms. On the surface, this seemed OK to me, but now I'm questioning myself whether this is indeed allowed, since the result of
seems rather nonsensical.