\sqrt{\frac{4}{3}} - \sqrt{\frac{3}{4}}=
\frac{2}{\sqrt{3}} + \frac{\sqrt{3}}{2}=
\frac{2 \sqrt{3}}{3} + \frac{\sqrt{3}}{2}=
\frac{4\sqrt{3}-3\sqrt{3}}{6}=
\frac{\sqrt{3}}{6}