$\dfrac{\sqrt{7}-3}{\sqrt{7}-1}+\sqrt{\dfrac{2}{4-\sqrt{7}}}$
$=\dfrac{\sqrt{7}-3}{\sqrt{7}-1}+\sqrt{\dfrac{4}{8-2\sqrt{7}}}$
$=\dfrac{\sqrt{7}-3}{\sqrt{7}-1}+\dfrac{2}{\sqrt{(\sqrt{7}-1)²}}$
$=\dfrac{\sqrt{7}-3+2}{\sqrt{7}-1}$
$=\dfrac{\sqrt{7}-1}{\sqrt{7}-1}$
$=1$