[tex]\displaystyle\bf\\\frac{6\sqrt{7}}{5\sqrt{8}}=\\\\=\frac{6\sqrt{7}}{5\sqrt{4\cdot2}}=\\\\=\frac{6\sqrt{7}}{5\cdot2\sqrt{2}}=~~~\Big|~Simplificam~cu~2.\\\\=\frac{3\sqrt{7}}{5\sqrt{2}}=~~~\Big|~Rationalizam~numitorul\\\\=\frac{3\sqrt{7}\cdot\sqrt{2}}{5\sqrt{2}\cdot\sqrt{2}}=\\\\=\frac{3\sqrt{14}}{5\cdot2}=\boxed{\bf\frac{3\sqrt{14}}{10}}[/tex]
