ĐK: \(x>0;a\ne1\)
\(\left(\dfrac{\sqrt{a}-2}{a-1}-\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}\right)\left(1+\dfrac{1}{\sqrt{a}}\right)\)
\(=\left[\dfrac{\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\sqrt{a}+2}{\left(\sqrt{a}+1\right)^2}\right].\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\left(\dfrac{\sqrt{a}-2}{\sqrt{a}-1}-\dfrac{\sqrt{a}+2}{\sqrt{a}+1}\right).\dfrac{1}{\sqrt{a}}\)
\(=\left[\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right].\dfrac{1}{\sqrt{a}}\)
\(=\left[\dfrac{a-\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{a+\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right].\dfrac{1}{\sqrt{a}}\)
\(=\dfrac{-2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}.\dfrac{1}{\sqrt{a}}\)
\(=\dfrac{-2}{a-1}\)
ĐKXĐ: \(\left\{{}\begin{matrix}a\ne1\\a>0\end{matrix}\right.\)
\(\left(\dfrac{\sqrt{a}-2}{a-1}-\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}\right)\left(1+\dfrac{1}{\sqrt{a}}\right)\)
\(=\left(\dfrac{\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}-\dfrac{\sqrt{a}+2}{\left(\sqrt{a}+1\right)^2}\right)\left(\dfrac{\sqrt{a}}{\sqrt{a}}+\dfrac{1}{\sqrt{a}}\right)\)
\(=\left(\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}-\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}\right).\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\left(\dfrac{a-\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}-\dfrac{a-\sqrt{a}+2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}\right).\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\dfrac{a-\sqrt{a}-2-a+\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}.\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\dfrac{-4}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)^2}.\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\dfrac{-4}{\left(\sqrt{a}-1\right).\sqrt{a}.\left(\sqrt{a}+1\right)}\)
