Question:

Find the limit algebraically:

Answer:

To find the limit algebraically, we can use direct substitution and simplify the expression. However, direct substitution gives us an indeterminate form ($\frac{0}{0}$) since both the numerator and denominator become zero when $x = 3$.

To resolve this indeterminate form, we can factorize the numerator and then cancel out the common factor with the denominator. Let's factorize the numerator:

Now, we can rewrite the expression:

Notice that the factor $(x - 3)$ appears in both the numerator and the denominator. We can cancel out this common factor:

Now we can substitute $x = 3$ into the expression:

Therefore, the limit algebraically is: