a: \(=\dfrac{15\sqrt{a}-11-3a-9\sqrt{a}+2\sqrt{a}+6-2a+2\sqrt{a}-3\sqrt{a}+3}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{-5a+7\sqrt{a}-2}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-1\right)}=\dfrac{-5\sqrt{a}+2}{\sqrt{a}+3}\)
b: P là số tự nhiên thì \(\left\{{}\begin{matrix}-5\sqrt{a}+2⋮\sqrt{a}+3\\a>=\dfrac{4}{25}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-5\sqrt{a}-15+17⋮\sqrt{a}+3\\a>=\dfrac{4}{25}\end{matrix}\right.\)
=>căn a+3=17
=>a=196
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