\(A=\left(\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\frac{1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right).\left(\frac{\sqrt{x}-2}{\sqrt{x}-1}\right)\)
\(=\frac{\left(x-2\sqrt{x}+1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}.\frac{\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)}\)
\(=\frac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}-1}{\sqrt{x}+2}\)
Để \(A< \frac{2}{3}\Rightarrow\frac{\sqrt{x}-1}{\sqrt{x}+2}< \frac{2}{3}\)
\(\Rightarrow3\sqrt{x}-3< 2\sqrt{x}+4\) (do \(\sqrt{x}+2>0\) \(\forall x\) xác định)
\(\Rightarrow\sqrt{x}< 7\Rightarrow x< 49\)
Kết hợp ĐKXĐ \(\Rightarrow\left\{{}\begin{matrix}0\le x< 49\\x\ne\left\{4;9\right\}\end{matrix}\right.\)
