\[\left( 3\sqrt{14} + \sqrt{7} \right)\ :\sqrt{7} - 2\sqrt{2} =\]
\[= 3\sqrt{14\ :7} + 1 - 2\sqrt{2} =\]
\[= 3\sqrt{2} + 1 - 2\sqrt{2} = 1 + \sqrt{2}.\]