a: \(A=\left(\dfrac{2a+1}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}-\dfrac{1}{\sqrt{a}-1}\right):\dfrac{a+\sqrt{a}+1-a-4}{a+\sqrt{a}+1}\)
\(=\dfrac{2a+1-a-\sqrt{a}-1}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\cdot\dfrac{a+\sqrt{a}+1}{\sqrt{a}-3}\)
\(=\dfrac{a-\sqrt{a}}{\left(\sqrt{a}-1\right)\cdot\left(\sqrt{a}-3\right)}=\dfrac{\sqrt{a}}{\sqrt{a}-3}\)
b: Để A là số nguyên dương thì \(\left\{{}\begin{matrix}a>9\\\sqrt{a}-3+3⋮\sqrt{a}-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a>9\\\sqrt{a}-3\in\left\{1;-1;3;-3\right\}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a>9\\a\in\left\{16;36;4;0\right\}\end{matrix}\right.\Leftrightarrow a\in\left\{16;36\right\}\)
