To simplify a rational expression where the terms have a greatest common factor (GCF), first factor out the GCF from both the numerator and the denominator, and then factor the remaining polynomials completely. Finally, divide out the common factors.

For instance, consider the expression: $\frac{3a^2 - 12ab + 12b^2}{6a^2 - 24b^2}$

First, factor out the GCF from the numerator (which is $3$) and the denominator (which is $6$): $\frac{3(a^2 - 4ab + 4b^2)}{6(a^2 - 4b^2)}$

Next, factor the resulting perfect square trinomial in the numerator and the difference of squares in the denominator: $\frac{3(a - 2b)(a - 2b)}{6(a + 2b)(a - 2b)}$

Rewrite $6$ as $3 \cdot 2$ to clearly identify all numerical common factors: $\frac{3(a - 2b)(a - 2b)}{3 \cdot 2(a + 2b)(a - 2b)}$

Remove the common factors of $3$ and $a - 2b$ to obtain the simplified expression: $\frac{a - 2b}{2(a + 2b)}$