Divide. \[ \frac{17 x^{2}+12 x}{2 x} \] Simplify your answer as much as possible.

To simplify the expression \( \frac{17 x^{2}+12 x}{2 x} \), we can break it down into two parts. We start by separating the numerator: \[ \frac{17 x^{2}}{2 x} + \frac{12 x}{2 x} \] Now, simplifying each term: 1. For the first term: \[ \frac{17 x^{2}}{2 x} = \frac{17}{2} x^{1} = \frac{17}{2} x \] 2. For the second term: \[ \frac{12 x}{2 x} = \frac{12}{2} = 6 \] Combining these results, we have: \[ \frac{17 x^{2}+12 x}{2 x} = \frac{17}{2} x + 6 \] Thus, the simplified expression is: \[ \frac{17}{2} x + 6 \]