a) ĐKXĐ : \(\)\(x\ge0\)
b) C=\(\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\right):\left(\dfrac{3\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{1}{\sqrt{x}}\right)\)
=\(\dfrac{\sqrt{x}\left(3-\sqrt{x}\right)+x+9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}:\dfrac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
=\(\dfrac{3\sqrt{x}-x+x-9}{\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)}:\dfrac{2\left(\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
=\(\dfrac{3\left(\sqrt{x}-3\right)}{\left(3+\sqrt{x}\right)\left(\sqrt{3}-\sqrt{x}\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+2\right)}\)
=\(\dfrac{-3\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)
c)giả sử C<-1
\(\Leftrightarrow\dfrac{-3\sqrt{x}\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}+1< 0\)\(\Leftrightarrow\dfrac{-3x+9\sqrt{x}+2\left(x+\sqrt{x}-6\right)}{2x+2\sqrt{x}-12}< 0\)
\(\Leftrightarrow\dfrac{-x+11\sqrt{x}-12}{2x+2\sqrt{x}-12}< 0\)
\(\Leftrightarrow2x+2\sqrt{x}-12< 0\)
\(\Leftrightarrow\)\(2x+6\sqrt{x}-4\sqrt{x}-12< 0\)\(\Leftrightarrow2\sqrt{x}\left(\sqrt{x}+3\right)-4\left(\sqrt{x}+3\right)< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}2\sqrt{x}-4< 0\\\sqrt{x}+3< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x< 4\\\sqrt{x}< -3\left(voly\right)\end{matrix}\right.\)
vậy \(0\le x< 4\)khi C<-1
