a: ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\notin\left\{1;9\right\}\end{matrix}\right.\)
b: Ta có: \(P=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-3}-\dfrac{\sqrt{a}+3}{\sqrt{a}-1}\right)\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-a+9}{\left(\sqrt{a}-3\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-3\right)\left(\sqrt{a}-1\right)}{8}\)
\(=\dfrac{\sqrt{a}-3}{8\sqrt{a}}\)
c: Để P<0 thì \(\sqrt{a}-3< 0\)
hay a<9
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}0< a< 9\\a\ne1\end{matrix}\right.\)
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