1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Limit Calc Test Problem

  1. Sep 5, 2010 #1
    1. The problem statement, all variables and given/known data

    This is a problem off a multiple choice practice test:
    lim t->3 ( 1/(t^2-3t) - 2/(t^2-9) =

    The solutions are:
    (a) 0 (b) -1/9 (c) -1/18 (d)1 (e) 1/3

    The correct answer is (c).

    Can someone explain to me how to solve it? Any help would be very appreciated. You don't need to explain how to do limits. I just need to know how to manipulate the equation so that it's not indeterminate.

    2. Relevant equations


    3. The attempt at a solution

    I tried multiplying by the conjugate with no success.
  2. jcsd
  3. Sep 5, 2010 #2


    User Avatar
    Science Advisor

    The first thing I would do is actually subtract the two fractions:
    [tex]\frac{1}{t^2- 3t}- \frac{2}{t^2- 9}= \frac{1}{t(t- 3)}- \frac{2}{(t- 3)(t+ 3)}[/tex]

    Clearly the "common denominator" is t(t- 3)(t+ 3):
    [tex]\frac{t+ 3}{t(t- 3)(t+ 3)}- \frac{2t}{t(t- 3)(t+ 3)}[/tex][tex]= \frac{t+ 3- 2t}{t(t- 3)(t+ 3)}= \frac{-t+ 3}{t(t- 3)(t+ 3)}= -\frac{t- 3}{t(t- 3)(t+ 3)}[/itex]
  4. Sep 5, 2010 #3
    Thank you!!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook