a) \(C=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\)
\(=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}-\frac{1}{\sqrt{x}}\right)\)
\(=\left(\frac{\sqrt{x}\left(3-\sqrt{x}\right)+x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{3\sqrt{x}+1-\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{3\sqrt{x}-x+x+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{3\sqrt{x}+9}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\left(\frac{3\left(\sqrt{x}+3\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right):\left(\frac{2\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\frac{3}{3-\sqrt{x}}\cdot\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+2\right)}\)
\(=\frac{3\sqrt{x}}{2\sqrt{x}+4}\)
b) Để C<-1 thì
\(\frac{3\sqrt{x}}{2\sqrt{x}+4}< -1\)
\(\Rightarrow3\sqrt{x}< -\left(2\sqrt{x}+4\right)\)
\(\Rightarrow3\sqrt{x}< -2\sqrt{x}-4\)
\(\Rightarrow3\sqrt{x}+2\sqrt{x}< -4\)
\(\Rightarrow5\sqrt{x}< -4\)
\(\Rightarrow\sqrt{x}< -\frac{4}{5}\)
\(\Rightarrow x< -\frac{16}{25}\)
