a: \(A=\dfrac{x-3\sqrt{x}-x-9}{x-9}:\dfrac{3\sqrt{x}+1+2\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3\left(\sqrt{x}+3\right)}{x-9}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{5\sqrt{x}-5}=\dfrac{-3\sqrt{x}}{5\sqrt{x}-5}\)
b: Để A<0 thì 5 căn x-5>0
=>x>1
\(A=\left(\dfrac{\sqrt{x}\left(3-\sqrt{x}\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}+\dfrac{x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\dfrac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}+\dfrac{2\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\dfrac{3\sqrt{x}-x+x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\dfrac{5\sqrt{x}-5}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\dfrac{3\left(\sqrt{x}+3\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{5\left(\sqrt{x}-1\right)}\)
\(=\dfrac{3\sqrt{x}}{5\left(1-\sqrt{x}\right)}\)
b.
\(B< 0\Rightarrow\dfrac{3\sqrt{x}}{5\left(1-\sqrt{x}\right)}< 0\)
\(\Rightarrow1-\sqrt{x}< 0\)
\(\Rightarrow x>1\)
Kết hợp ĐKXĐ \(\Rightarrow\left\{{}\begin{matrix}x>1\\x\ne9\end{matrix}\right.\)
