On 9/29/2013 8:45 AM, Michael F. Stemper wrote: > On 09/28/2013 04:20 PM, Hetware wrote: >> On 9/28/2013 4:24 PM, Richard Tobin wrote: >>> In article <9cSdnYGhH7CMpNrPnZ2dnUVZ_sCdnZ2d@megapath.net>, >>> Hetware <firstname.lastname@example.org> wrote: > >>>> So the answer is consensus among mathematicians holds that F(t) = >>>> (t^2 - >>>> 9)/(t - 3) is undefined at t=3? >>> >>> Yes. >>> >>>> Perhaps what I should have said at the >>>> outset is something along the lines of: on any given day, if I'm >>>> setting >>>> up an equation in physics, and produce an expression such as F(t) = >>>> (t^2 >>>> - 9)/(t - 3), I treat it as t+3, and do not expect any adverse >>>> consequence from doing so. >>> >>> Your simplification is not valid for t=3. > >> I believe most mathematicians solving for x as a function of t given >> >> t^2 - 9 = x (t - 3) >> >> would not hesitate to factor the left hand side and divide both sides by >> t - 3 without treating t = 3 as a special case. > > This is high-school stuff. Literally. > > I just pulled my text from Algebra II (tenth grade) off the shelf. > > Turning to Section 3.6, "Rational Expressions: Reduction to Simplest > Form", I see: > > It should be observed that since division by zero is excluded > as an operation, a fraction whose denominator is zero has no > meaning. For example, the fraction 9/(y-7) has no meaning > when y=7. Also, the fraction (x+5)/(x^2-9) has no meaning > when x=3 or x=-3. > > We sometimes encounter fractions such as (x-3)/(3-x) > (x!=3). [...] > > The authors then proceed to work through several examples of fractions > with polynomials in the numerator and denominator. In every case, when > the fraction is specified, they include: > > where (d(x)!=0) > > (I'm using d(x) here to represent whatever the denominator polynomial > happens to be.) > > If your high school math classes neglected to point out that this > exclusion is necessary, they were faulty. However, the errors and > omissions of your past teachers do not change the fact that it is. > > >  _Algebra and Trigonometry: A Modern Approach_, Peters & Schaaf, > van Nostrand, (c) 1965
What I am saying is that if I encountered an expression such as (t^2-9)/(t-3) in the course of solving a problem in applied math, I would not hesitate to treat it as t+3 and not haggle over the case where t = 3.
If I wanted to express x as a function of t given (t^2-9) = x(t-3), I would have no compunction about "dividing out" t-3. Since I can arrive at the same result through a different method, I do not see why treating (t-3)/(t-3) = 1 in this context is an error.
I don't feel a twinge of unease. I have no experience of it leading to an incorrect final result. If I encounter something of the form f(t)/(3-t) and the problem domain includes t = 3, I anticipate a problem at t = 3. If I can fiddle with f(t) and factor out 3-t, I simply cancel them out, and keep going.