a, Với x >= 0 ; x khác 4
\(=\frac{x-3\sqrt{x}+2-\left(x+4\sqrt{x}+3\right)-x-5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)
\(=\frac{-3\sqrt{x}-3-x-4\sqrt{x}-3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}=\frac{-7\sqrt{x}-6-x}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)
\(=\frac{-\left(\sqrt{x}+1\right)\left(\sqrt{x}+6\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}=\frac{-\sqrt{x}-6}{\sqrt{x}-2}\)
b, \(Q+1>0\Leftrightarrow\frac{-\sqrt{x}-6+\sqrt{x}-2}{\sqrt{x}-2}>0\Leftrightarrow\frac{-8}{\sqrt{x}-2}>0\)
\(\Rightarrow\sqrt{x}-2< 0\Leftrightarrow x< 4\Rightarrow0\le x< 4\)
c, \(\frac{-\left(\sqrt{x}+6\right)}{\sqrt{x}-2}=\frac{-\left(\sqrt{x}-2+8\right)}{\sqrt{x}-2}=-1-\frac{8}{\sqrt{x}-2}\)
\(\Rightarrow\sqrt{x}-2\inƯ\left(8\right)=\left\{\pm1;\pm2;\pm4;\pm8\right\}\)
| \(\sqrt{x}-2\) | -1 | 1 | -2 | 2 | -4 | 4 | -8 | 8 |
| x | 1 | 9 | 0 | 16 | loại | 36 | loại | 100 |
