$Đk:a>0;a\ne1$
$B=\bigg(\dfrac{6}{a-1}+\dfrac{10-2\sqrt{a}}{a\sqrt{a}-a-\sqrt{a}+1}\bigg).\dfrac{(\sqrt{a}-1)^2}{4\sqrt{a}}\\ =\dfrac{6(\sqrt{a}-1)+10-2\sqrt{a}}{(\sqrt{a}-1)^2(\sqrt{a}+1)}.\dfrac{(\sqrt{a}-1)^2}{4\sqrt{a}}\\ =\dfrac{4(\sqrt{a}+1)}{(\sqrt{a}-1)^2(\sqrt{a}+1)}.\dfrac{(\sqrt{a}-1)^2}{4\sqrt{a}}\\ =\dfrac{1}{\sqrt{a}}$