Let's solve the problem:

The given rational expression is:

$\frac{x^2 - 4x}{6x - 24}$

Step 1: Factor the numerator and denominator

Numerator:

$x^2 - 4x = x(x - 4)$

Denominator:

$6x - 24 = 6(x - 4)$

Step 2: Simplify the expression

Substituting the factored forms into the expression: $\frac{x(x - 4)}{6(x - 4)}$

Cancel out the common factor $(x - 4)$ (as long as $x \neq 4$): $\frac{x}{6}$

Final Answer:

$\frac{x}{6}$

Let me know if you'd like further explanation!

5 Related Questions:

1. How do you identify common factors in rational expressions?
2. What happens if the denominator equals zero in a rational expression?
3. Can you explain how to simplify rational expressions with multiple variables?
4. How do you handle rational expressions that cannot be factored?
5. What are the steps to multiply or divide rational expressions?

Tip:

Always check for restrictions in the variable (e.g., $x \neq 4$ here) when simplifying rational expressions.