a)
\(M=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{2\sqrt{a}-1}{a-\sqrt{a}}\right).\dfrac{2\sqrt{a}}{a-1}\\ M=\left(\dfrac{\sqrt{a}.\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}-\dfrac{2\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right).\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ M=\dfrac{a-2\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ M=\dfrac{\left(\sqrt{a}-1\right)^2.2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ M=\dfrac{2}{\sqrt{a}+1}\)
b)
\(M< 0\Leftrightarrow\dfrac{2}{\sqrt{a}+1}< 0\\ \Leftrightarrow\sqrt{a}+1< 0\\ \sqrt{a}< -1\left(vô\:lí\right)\)
vậy không có giá trị nào của a để M<0
