1. **Stating the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel common factors. 3. **Factor numerator:** $$2x^2 - 8 = 2(x^2 - 4) = 2(x-2)(x+2)$$. 4. **Rewrite denominator:** $$4x = 4x$$. 5. **Rewrite expression:** $$\frac{2(x-2)(x+2)}{4x}$$. 6. **Simplify coefficients:** $$\frac{2}{4} = \frac{1}{2}$$. 7. **Final simplified form:** $$\frac{(x-2)(x+2)}{2x}$$. This is the simplified expression, valid for $$x \neq 0$$ to avoid division by zero.