a, ĐKXĐ: x>0 (1)
b,T= (\(\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+1\right)+6\sqrt{x}-9\sqrt{x}\left(\sqrt{x}+1\right)}{3\sqrt{x}\left(\sqrt{x}+1\right)}\)).(\(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\))+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{x+3\sqrt{x}+2+6\sqrt{x}-9x-9\sqrt{x}}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{2-8x}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2-4\sqrt{x}}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\left(\frac{2\left(1-2\sqrt{x}\right)\left(1+2\sqrt{x}\right)}{3\sqrt{x}\left(\sqrt{x}+1\right)}\right)\).\(\left(\frac{\sqrt{x}+1}{2\left(1-2\sqrt{x}\right)}\right)\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\)
= \(\frac{1+2\sqrt{x}}{3\sqrt{x}}\)+\(\frac{x-3\sqrt{x}-1}{3\sqrt{x}}\) = \(\frac{x-\sqrt{x}}{3\sqrt{x}}\)=\(\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{3\sqrt{x}}\)=\(\frac{\sqrt{x}-1}{3}\)
c, Để T<0 \(\Leftrightarrow\)\(\frac{\sqrt{x}-1}{3}\) <0 \(\Leftrightarrow\) \(\sqrt{x}\)-1<0 \(\Leftrightarrow\) \(\sqrt{x}\)<1\(\Leftrightarrow\) x<1 mà do ĐK (1)
=> Để T<0 \(\Leftrightarrow\) 0<x<1