ĐKXĐ: \(a>0;a\ne1\)
\(\left(\frac{1}{\sqrt{a}+1}-\frac{1}{a-\sqrt{a}}\right):\frac{\sqrt{a}-1}{\left(\sqrt{a}+1\right)^2}\)
\(=\left[\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}-\frac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right].\frac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}-1}\)
\(=\frac{\sqrt{a}\left(\sqrt{a}-1\right)-\left(\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}.\frac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}-1}\)
\(=\frac{\left(a-2\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)^2}\)
