Problem:

Find the limit algebraically:

Explanation:

To find the limit algebraically, we need to evaluate the function as $x$ approaches the given value.

First, let's substitute the given value $x = 2$ into the expression:

Simplifying, we obtain:

Note that dividing by zero is undefined, so we need to find an alternative approach to evaluate this limit.

Since we have a numerator of $x^2 - 4$, we can factor it as a difference of squares:

We can see that the $(x - 2)$ term cancels out:

Leaving us with just:

Now, we can substitute $x = 2$ into this simplified expression:

Therefore, the limit as $x$ approaches $2$ is equal to $4$.

Answer: