2.2.2 \( \frac{6 x^{3}-8 x^{2}+2 x+10}{2 x} \)

To simplify the expression \( \frac{6 x^{3}-8 x^{2}+2 x+10}{2 x} \), you can start by dividing each term in the numerator by \( 2x \): 1. \( \frac{6x^3}{2x} = 3x^2 \) 2. \( \frac{-8x^2}{2x} = -4x \) 3. \( \frac{2x}{2x} = 1 \) 4. \( \frac{10}{2x} = \frac{5}{x} \) Putting it all together, you get \( 3x^2 - 4x + 1 + \frac{5}{x} \). Simplifying further gives you the final result of \( 3x^2 - 4x + 1 + \frac{5}{x} \). Now you have a neat expression! But make sure you keep an eye on the domain—this expression is undefined for \( x = 0 \) since you can't divide by zero. So, no zero for you!