1. The problem is to simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. The formula used here is to simplify fractions by factoring and canceling common factors. 3. First, factor the numerator: $$2x^2 - 8 = 2(x^2 - 4)$$ 4. Recognize that $x^2 - 4$ is a difference of squares: $$x^2 - 4 = (x - 2)(x + 2)$$ 5. So the numerator becomes: $$2(x - 2)(x + 2)$$ 6. The expression is now: $$\frac{2(x - 2)(x + 2)}{4x}$$ 7. Factor the denominator: $$4x = 2 \times 2 \times x$$ 8. Cancel the common factor 2 from numerator and denominator: $$\frac{\cancel{2}(x - 2)(x + 2)}{\cancel{2} \times 2 \times x} = \frac{(x - 2)(x + 2)}{2x}$$ 9. The simplified expression is: $$\frac{(x - 2)(x + 2)}{2x}$$ 10. This is the simplest form unless further expansion or specific values for $x$ are given. Final answer: $$\frac{(x - 2)(x + 2)}{2x}$$