$(\sqrt\frac{3}{4}-\sqrt\frac{3}{9})\sqrt\frac{6}{50}=\sqrt\frac{3}{4}\times \sqrt\frac{6}{50}-\sqrt\frac{3}{9}\times \sqrt\frac{6}{50}=\sqrt \frac{18}{200}- \sqrt \frac{18}{450}=\sqrt \frac{9}{100}-\sqrt \frac{1}{25}=\frac{3}{10}-\frac{1}{5}=\frac{3}{10}-\frac{2}{10}=\frac{1}{10}$