text: find all numbers for which the rational expression is not defined.? x2 - 49                             (x2 means x squared) ______________                   x2 - 10x + 24 factoring the denominator gives (x-4)(x-6)  by plugging these values back into the denominator, we see   x=4  4^2 - 10(4) + 24 = 16 - 40 + 24 = 0  x=6  6^2 - 10(6) + 24 = 36 - 60 + 24 = 0  any number with 0 in the denominator is invalid (divide by 0), results in a vertical line at x=4 and x=6, and thus is undefined.  as for the calculus:  lim x->inf (x^2 - 49 -:- x^2 - 10x + 24) by l'hospital's rule of taking the derivatives of both numerator and denominator;  lim x->inf (2x -:- 2x-10)  2 -:- 2 = 1.  thus it is not an undefined limit.    therefore 4 and 6 are the only undefined answers.