1. The problem is to simplify the expression $\frac{2x^2 - 8}{4x}$. 2. The formula used here is simplifying rational expressions by factoring and canceling common factors. 3. First, factor the numerator: $$2x^2 - 8 = 2(x^2 - 4) = 2(x - 2)(x + 2)$$ 4. Rewrite the expression: $$\frac{2(x - 2)(x + 2)}{4x}$$ 5. Simplify the fraction by canceling common factors: $$\frac{\cancel{2}(x - 2)(x + 2)}{\cancel{4}x} = \frac{(x - 2)(x + 2)}{2x}$$ 6. The simplified expression is: $$\frac{(x - 2)(x + 2)}{2x}$$ 7. This means the original expression simplifies to $\frac{(x - 2)(x + 2)}{2x}$, which is easier to work with or evaluate for specific values of $x$.