\(\dfrac{3\sqrt{3}-1}{\sqrt{3}+\sqrt{2}}\\ =\dfrac{\left(3\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}{3-2}\\ =\left(3\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)\\ =9-3\sqrt{6}-\sqrt{3}+\sqrt{2}\)

ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)

\(M=\left(\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}+\dfrac{\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)^2}\\ =\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}+1}\\ =\dfrac{\sqrt{a}-1}{\sqrt{a}}\)