I'm reading a 1953 edition of Thomas's Calculus and Analytic Geometry. In it he states that given: F(t) = (t^2-9)/(t-3)
F(t) = (t-3)(t+3)/(t-3) = t+3 when t!=3.
But F(t) is not defined at t=3 because it evaluates to 0/0.
If someone were to ask me if (t^2-9)/(t-3) is defined when t=3, I would say it is because it can be simplified to t+3. Am I (and/or Thomas) engaging in meaningless hair-splitting regarding the question of F(3) being defined?