Question:

Find the limit algebraically:

Explanation:

To find the limit, we can try direct substitution. Plugging in $x = 3$ gives us:

However, this expression is of the form $\frac{0}{0}$ which is undefined.

To proceed, we can simplify the expression by factoring the numerator:

Notice that the term $(x - 3)$ appears in both the numerator and denominator and can be canceled out:

Leaving us with:

Now, we can evaluate the limit by direct substitution since the denominator no longer causes an undefined expression:

Thus, the limit of the given expression as $x$ approaches 3 is 6.

Answer:

The limit,