$(\sqrt{\dfrac{1}{7}}-3\sqrt{7}+2\sqrt{343}):\sqrt{7}$
$=(\dfrac{\sqrt{7}}{7}-3\sqrt{7}+14\sqrt{7}):\sqrt{7}$
$=(\dfrac{\sqrt{7}}{7}+11\sqrt{7}):\sqrt{7}$
$=(\dfrac{\sqrt{7}}{7}+\dfrac{77\sqrt{7}}{7}):\sqrt{7}$
$=\dfrac{78\sqrt{7}}{7}:\sqrt{7}$
$=\dfrac{78\sqrt{7}}{7}.\dfrac{1}{\sqrt{7}}$
$=\dfrac{78}{7}$