# Homework Help: Limit Calc Test Problem

1. Sep 5, 2010

### nick850

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

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

NA

3. The attempt at a solution

I tried multiplying by the conjugate with no success.

2. Sep 5, 2010

### HallsofIvy

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

Clearly the "common denominator" is t(t- 3)(t+ 3):
$$\frac{t+ 3}{t(t- 3)(t+ 3)}- \frac{2t}{t(t- 3)(t+ 3)}$$[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]

3. Sep 5, 2010

Thank you!!