1: ĐKXĐ: \(\left\{{}\begin{matrix}a>=0\\a< >1\end{matrix}\right.\)
\(M=\left(\dfrac{\sqrt{a}}{\sqrt{a}+1}+\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{1-a}\right):\left(\sqrt{a}+1\right)\)
\(=\left(\dfrac{\sqrt{a}}{\sqrt{a}+1}+\dfrac{1}{\sqrt{a}-1}+\dfrac{2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right):\left(\sqrt{a}+1\right)\)
\(=\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)+\sqrt{a}+1+2\sqrt{a}}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}\)
\(=\dfrac{a-\sqrt{a}+3\sqrt{a}+1}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}=\dfrac{1}{\sqrt{a}-1}\)
2: Để M<0 thì \(\dfrac{1}{\sqrt{a}-1}< 0\)
=>\(\sqrt{a}-1< 0\)
=>\(\sqrt{a}< 1\)
=>0<=a<1
