`1)`\(P=\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right).\dfrac{1}{2a\sqrt{a}}\)
\(P=\dfrac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2+4\sqrt{a}\left(a-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}.\dfrac{1}{2a\sqrt{a}}\)
\(P=\dfrac{4\sqrt{a}+4\sqrt{a}\left(a-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}.\dfrac{1}{2a\sqrt{a}}\)
\(P=\dfrac{4a\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}.\dfrac{1}{2a\sqrt{a}}\)
\(P=\dfrac{2}{a-1}\)
`2)`\(P=a\)
\(\Leftrightarrow\dfrac{2}{a-1}=a\)
\(\Leftrightarrow a^2-a-2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=-1\left(ktm\right)\\a=2\left(tm\right)\end{matrix}\right.\)
