\(P=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right)\div\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(=\left[\dfrac{\left(\sqrt{a}\right)-\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]\div\left[\dfrac{\left(a-1\right)-\left(a-2\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}\right]\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\times\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{1}\)
\(=\dfrac{\sqrt{a}-2}{\sqrt{a}}\)
(^~^)
\(\dfrac{\sqrt{a}-2}{\sqrt{a}}>\dfrac{1}{6}\)
\(\Leftrightarrow6\sqrt{a}-12>\sqrt{a}\)
\(\Leftrightarrow5\sqrt{a}>12\)
\(\Leftrightarrow a>\dfrac{144}{25}\)
