Determine the limit \begin{equation} \lim_{x\to 3}\,\frac{x^2-9}{x-3}. \end{equation}

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Lesson Parent: 
Function Limits V: Properties of Function Limits
Problem: 

Determine the limit
\begin{equation}
\lim_{x\to 3}\,\frac{x^2-9}{x-3}.
\end{equation}

Answer: 

6

SAMPLE SOLUTION

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Solution: 

First, let's do some algebra:

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We can do this because our formal definition of a function limit says that $x$ is never equal to $3$. In other words we know that $x-3$ will never be zero so we can do the division. So whenever you see a function with something going to zero in the denominator then check if it can be cancelled by something in the numerator.

Now that this is the sum of two known limits (see this and this) then we know that

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