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. **Factor denominator:** $4x = 2 \times 2x$. 6. **Cancel common factor 2:** $$\frac{\cancel{2}(x-2)(x+2)}{2 \times 2x} = \frac{(x-2)(x+2)}{2x}$$ 7. **Final simplified form:** $$\frac{(x-2)(x+2)}{2x}$$ This is the simplest form unless further expansion or restrictions on $x$ are given.