ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)
\(A=\left(\dfrac{\sqrt{a}-2}{a+2\sqrt{a}+1}-\dfrac{\sqrt{a}+2}{a-1}\right)\cdot\dfrac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}}\)
\(=\left(\dfrac{\sqrt{a}-2}{\left(\sqrt{a}+1\right)^2}-\dfrac{\sqrt{a}+2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\cdot\dfrac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}}\)
\(=\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}+2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}}\)
\(=\dfrac{a-3\sqrt{a}+2-a-3\sqrt{a}-2}{\sqrt{a}\left(\sqrt{a}-1\right)}=\dfrac{-6\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\)
\(=-\dfrac{6}{\sqrt{a}-1}\)
