Let's simplify the expression:

$\frac{8(x - 3)^2}{4(x - 3)}$

First, notice that both the numerator and denominator contain a factor of $(x - 3)$. We can cancel out one $(x - 3)$ from the numerator and denominator, as long as $x \neq 3$ (since division by zero is undefined).

After canceling, we have:

$\frac{8(x - 3)}{4}$

Now simplify the coefficients. The fraction $\frac{8}{4}$ simplifies to 2:

$2(x - 3)$

Thus, the simplified expression is:

$2(x - 3)$

Do you need further clarification on any part of the simplification?

Here are 5 related questions you might find interesting:

1. How would this simplify if the numerator were $8(x - 3)^3$?
2. What happens if $x = 3$ in this expression?
3. How do you factor the expression $2(x - 3)$?
4. What is the derivative of $2(x - 3)$?
5. How do you evaluate $2(x - 3)$ for $x = 5$?

Tip: Always check for common factors in both the numerator and denominator before simplifying algebraic fractions.