Question: find all numbers for which the rational expression is not defined.? x2 - 49                             (x2 means x squared)\n______________                 \n\nx2 - 10x + 24

Answer: Factoring the denominator gives (x-4)(x-6)\n\nBy plugging these values back into the denominator, we see \n\nx=4\n\n4^2 - 10(4) + 24 = 16 - 40 + 24 = 0\n\nx=6\n\n6^2 - 10(6) + 24 = 36 - 60 + 24 = 0\n\nAny 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.\n\nAs for the calculus:\n\nlim x->inf (x^2 - 49 -:- x^2 - 10x + 24) by L'Hospital's Rule of taking the derivatives of both numerator and denominator;\n\nlim x->inf (2x -:- 2x-10)\n\n2 -:- 2 = 1.  Thus it is not an undefined limit.  \n\nTherefore 4 and 6 are the only UNDEFINED answers.
This question from the Yahoo Q&A forum is categorized in the topic: Sports