$1)\frac{12}{2\sqrt{5}}=\frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{\sqrt{5}.\sqrt{5}}=\frac{6\sqrt{5}}{5}$
$2)\frac{3}{2\sqrt{5}}=\frac{3.2\sqrt{5}}{2\sqrt{5}.2\sqrt{5}}=\frac{6\sqrt{5}}{20}=\frac{3\sqrt{5}}{10}$
$3)\frac{6\sqrt{2}-7\sqrt{7}}{\sqrt{6}}=\frac{\sqrt{6}(6\sqrt{2}-7\sqrt{7})}{\sqrt{6}.\sqrt{6}}=\frac{-7\sqrt{42}+12\sqrt{3}}{6}$