Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 60

$\dfrac{x^3}{2\sqrt{3x}}$

Rationalizing the numerator of $ \dfrac{\sqrt{3x^5}}{6} $ results to \begin{array}{l} \dfrac{\sqrt{x^4\cdot3x}}{6} \\\\= \dfrac{x^2\sqrt{3x}}{6} \\\\= \dfrac{x^2\sqrt{3x}}{6} \cdot \dfrac{\sqrt{3x}}{\sqrt{3x}} \\\\= \dfrac{x^2\sqrt{9x^2}}{6\sqrt{3x}} \\\\= \dfrac{x^2\cdot3x}{6\sqrt{3x}} \\\\= \dfrac{3x^3}{6\sqrt{3x}} \\\\= \dfrac{x^3}{2\sqrt{3x}} .\end{array}