To simplify the expression \(\frac{\sqrt{18x^3}}{\sqrt{2x}}\), we can use the property of square roots that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\). Therefore, we can rewrite the expression as:
\[ \frac{\sqrt{18x^3}}{\sqrt{2x}} = \sqrt{\frac{18x^3}{2x}} \]
Now, simplify the fraction inside the square root:
\[ \frac{18x^3}{2x} = \frac{18}{2} \cdot \frac{x^3}{x} = 9x^2 \]
So we have:
\[ \sqrt{\frac{18x^3}{2x}} = \sqrt{9x^2} \]
Now, we can take the square root:
\[ \sqrt{9x^2} = \sqrt{9} \cdot \sqrt{x^2} = 3x \]
Thus, the simplified expression is:
\[ \frac{\sqrt{18x^3}}{\sqrt{2x}} = 3x \]
Therefore, the final answer is:
\[ 3x \]