\(a.\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-4}=\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\sqrt{2}-4}=\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{-2\sqrt{2}\left(\sqrt{2}-1\right)}=-\dfrac{\sqrt{3}}{2}\)
\(b.\dfrac{a^2\sqrt{b}-\sqrt{ab^3}}{\sqrt{a^3b^2}-b^2}=\dfrac{a^2\sqrt{b}-b\sqrt{ab}}{ab\sqrt{a}-b^2}=\dfrac{\sqrt{ab}\left(a\sqrt{a}-b\right)}{b\left(a\sqrt{a}-b\right)}=\sqrt{\dfrac{a}{b}}\left(a;b>0\right)\)
\(c.\dfrac{a^3-2\sqrt{2}}{a-\sqrt{2}}=\dfrac{\left(a-\sqrt{2}\right)\left(a^2+a\sqrt{2}+2\right)}{a-\sqrt{2}}=a^2+a\sqrt{2}+2\left(a\ne\sqrt{2}\right)\)
\(d.\sqrt{18}-\sqrt{8}+\dfrac{1}{4}\sqrt{2}=3\sqrt{2}-2\sqrt{2}+\dfrac{1}{4}\sqrt{2}=\left(\dfrac{1}{4}+1\right)\sqrt{2}=\dfrac{5}{4}\sqrt{2}\)
