Does 9/sqrt3(10) =sqrt3(10)/10
$$\frac{9}{\sqrt3}\times 10 \\\\
=\frac{9}{\sqrt3}\times \frac{10}{1} \\\\
=\frac{90}{\sqrt3} \\\\
=\frac{90}{\sqrt3}\times \frac{\sqrt3}{\sqrt3} \\\\
=\frac{90\sqrt3}{\sqrt3\times\sqrt3} \\\\
=\frac{90\sqrt3}{3} \\\\
=30\sqrt3$$