Limits of t^2-9/t-3: Factoring & Substitution

[screamtrumpet]

Homework Statement

lim t^2-9/t-3
x>3

Homework Equations

The Attempt at a Solution

I factored it into (t-3)(t+3)/(t-3)
i then canceled out the (t-3)'s and substituted 3 to get 6 is this correct?

 

[rakalakalili]

Assuming you made a typo and your problem is the limit as t -> 3, then yes, what you did is correct. You can only ever cancel an expression with a variable (such as (t-3)) if you are sure that it is not going to be zero. In this case, we are taking the limit as t goes to 3, so (t-3) is never actually equal to 0. Thus, we can cancel (t-3) and you are correct.

 

[screamtrumpet]

Thanks!