Question:

Find the limit algebraically:

Answer:

To find the limit of a rational function as $x$ approaches a certain value, we can simplify the function by factoring both the numerator and the denominator and then canceling out any common factors.

Given:

First, let's factor the numerator and denominator:

Now, we can cancel out the common factor of $(x - 3)$:

Now we can substitute $x = 3$ into the simplified function to find the limit:

Therefore, the limit of the function as $x$ approaches 3 is $\frac{2}{9}$.