To rationalize the denominator of the expression \( \frac{3}{2 \sqrt{3}} \), you want to eliminate the square root from the denominator. You can achieve this by multiplying both the numerator and the denominator by \( \sqrt{3} \).
Here's how it's done:
\[ \frac{3}{2 \sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3 \sqrt{3}}{2 \sqrt{3} \cdot \sqrt{3}} \]
Now, calculate the denominator:
\[ 2 \sqrt{3} \cdot \sqrt{3} = 2 \cdot 3 = 6 \]
So the expression becomes:
\[ \frac{3 \sqrt{3}}{6} \]
Now you can simplify the fraction:
\[ \frac{3 \sqrt{3}}{6} = \frac{\sqrt{3}}{2} \]
Thus, the final result is:
\[ \frac{\sqrt{3}}{2} \]