1. **State 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 expression:** $$\frac{2(x-2)(x+2)}{4x}$$. 5. **Simplify denominator:** $$4x = 2 \times 2x$$. 6. **Cancel common factor 2:** $$\frac{\cancel{2}(x-2)(x+2)}{\cancel{2} \times 2x} = \frac{(x-2)(x+2)}{2x}$$. 7. **Final simplified form:** $$\frac{(x-2)(x+2)}{2x}$$. This is the simplest form unless further factorization or domain restrictions are specified.