a, \(A=\left(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{a+\sqrt{a}}\right):\frac{a+2}{a-2}\) \(\left(a>0;a\ne2\right)\)
\(=\left[\frac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}-\frac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}\right]:\frac{a+2}{a-2}\)
\(=\frac{a+\sqrt{a}+1-a+\sqrt{a}-1}{\sqrt{a}}.\frac{a-2}{a+2}\)
\(=\frac{2\sqrt{a}}{\sqrt{a}}.\frac{a-2}{a+2}\)
\(=\frac{2\left(a-2\right)}{a+2}\)
b, Để: \(A=1\Leftrightarrow\frac{2\left(a-2\right)}{a+2}=1\)
\(\Rightarrow\frac{2a-4-a-2}{a+2}=0\)
\(\Rightarrow\frac{a-6}{a+2}=0\)
\(\Rightarrow a-6=0\)
\(\Rightarrow a=6\left(tm\right)\)
Vậy...........................