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

• screamtrumpet
In summary, the conversation discussed the process of factoring and canceling terms in a limit problem. It was determined that the approach taken was correct, as long as the variable in the expression being cancelled is not equal to 0.
screamtrumpet

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

## 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?

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.

Thanks!

## What is the equation t^2-9/t-3?

The equation t^2-9/t-3 is a rational expression that can be simplified by factoring and substitution.

## What is factoring and how does it apply to t^2-9/t-3?

Factoring is the process of breaking down an expression into its smaller, simpler parts. In the case of t^2-9/t-3, we can factor out the common factor of (t-3) from both the numerator and denominator to simplify the expression.

## How can substitution be used to simplify t^2-9/t-3?

Substitution involves replacing a variable in an equation with a given value. In the case of t^2-9/t-3, we can substitute t=3 into the equation to simplify it to 0/0, which is undefined.

## What is the significance of the limits of t^2-9/t-3?

The limits of t^2-9/t-3 represent the values that t approaches as it gets closer and closer to a certain value. In this case, the limit is undefined as t approaches 3, since the expression becomes 0/0 which is undefined.

## How can factoring and substitution be used to find the limits of t^2-9/t-3?

By factoring and simplifying the expression, we can determine which values of t would result in an undefined expression. Then, we can use substitution to evaluate the expression at those values and determine the limits of t^2-9/t-3.

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