Simplify. \( \frac{2 x^{2}-8 x}{2 x} \)

To simplify the expression \( \frac{2 x^{2}-8 x}{2 x} \), first, we can factor out the numerator: \( 2x^2 - 8x = 2x(x - 4) \). Now, substituting this back into the fraction gives us: \( \frac{2x(x - 4)}{2x} \). The \( 2x \) in the numerator and the \( 2x \) in the denominator cancel out, provided \( x \neq 0 \): \( x - 4 \). Thus, the simplified expression is: \( x - 4 \).