To find $\frac{f(x)}{g(x)}$, we'll first substitute the given functions $f(x)$ and $g(x)$ and then simplify.

Given: $f(x) = x^2 - x - 6$ $g(x) = x - 3$

Now, we want to find: $\frac{f(x)}{g(x)} = \frac{x^2 - x - 6}{x - 3}$

To simplify this, we can try to factor the numerator $x^2 - x - 6$.

The numerator $x^2 - x - 6$ factors as: $x^2 - x - 6 = (x - 3)(x + 2)$

So we have: $\frac{x^2 - x - 6}{x - 3} = \frac{(x - 3)(x + 2)}{x - 3}$

As long as $x \neq 3$, the $x - 3$ terms cancel out, giving: $\frac{f(x)}{g(x)} = x + 2$

Final Answer: $\frac{f(x)}{g(x)} = x + 2 \quad \text{for} \quad x \neq 3$

Would you like further details or have any questions about this solution?

Here are some related questions you might find interesting:

1. How do you factor a quadratic expression like $x^2 - x - 6$?
2. What happens if $x = 3$ in the expression $\frac{f(x)}{g(x)}$?
3. Can you find the remainder when $f(x)$ is divided by $g(x)$?
4. How does the graph of $f(x)$ compare to the graph of $g(x)$?
5. What is the domain of the function $\frac{f(x)}{g(x)}$?

Tip: When simplifying expressions, always check if there are restrictions on the values of $x$ due to potential division by zero.