\(M=\left(\dfrac{\sqrt{a}}{\sqrt{a}+1}-\dfrac{\sqrt{a}}{\sqrt{a}-1}+\dfrac{2\sqrt{a}-4}{a-1}\right):\dfrac{1}{\sqrt{a}+1}\)
ĐKXĐ: \(a\ge0;a\ne1\)
\(M=\left[\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}-\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}+\dfrac{2\sqrt{a}-4}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right].\left(\sqrt{a}+1\right)\)
\(=\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)-\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{a}-4}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}.\left(\sqrt{a}+1\right)\)
\(=\dfrac{a-\sqrt{a}-a-\sqrt{a}+2\sqrt{a}-4}{\sqrt{a}-1}\)
\(=\dfrac{-4}{\sqrt{a}-1}\)
