1. **State the problem:** Simplify the expression $\frac{2x^2 - 8}{4x}$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel common factors. 3. **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:** $$\frac{\cancel{2}(x-2)(x+2)}{\cancel{4}x} = \frac{(x-2)(x+2)}{2x}$$ 6. **Final simplified form:** $$\frac{(x-2)(x+2)}{2x}$$ This is the simplest form unless further factorization or restrictions on $x$ are given.