Simplify Rational 4A3Fb6

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 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:** $$\frac{(x - 2)(x + 2)}{2x}$$. **Explanation:** We factored the numerator to find common factors with the denominator and canceled the common factor 2, simplifying the expression step-by-step.