From: C Y <smustudent1 at yahoo>
in the case of something like:
(x + 2) (x + 1)
---------------
x + 1
Maxima will simplify this to x+2. But, as written, doesn't this
expression have a hole at x=-1?
See l'Ho^pital's Rule in your favorite reference. It says that an
expression f(x)/g(x) where both f(x) and g(x) go to zero at some x0,
the limit as x->x0 is f'(x0)/g'(x0).
This is true except for functions that are so badly behaved that you
wouldn't normally want to call them functions. [Of course, I'm
writing this as a music theorist, not a mathematician, and we music
theorists have been quite happy for the last 2500 years with nothing
much to work with except ratios of small integers, and no clear notion
of zero at all. That's why we call two identical pitches a "unison",
two pitches one step apart a "second", and two pitches two steps apart
a "third". Add two thirds and you get a fifth.]