An example of multiplying rational expressions is simplifying $\frac{2x}{x^2 - 7x + 12} \cdot \frac{x^2 - 9}{6x^2}$.

Step 1. Factor each numerator and denominator completely: $\frac{2x}{(x - 3)(x - 4)} \cdot \frac{(x - 3)(x + 3)}{6x^2}$. Step 2. Multiply the numerators and denominators: $\frac{2x(x - 3)(x + 3)}{6x^2(x - 3)(x - 4)}$. Step 3. Simplify by dividing out the common factors $(x - 3)$ and $2x$. The simplified result is $\frac{x + 3}{3x(x - 4)}$.