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\[ \frac{2\left(\sqrt{2}+\sqrt{6} \right)}{3\sqrt{2+\sqrt{3}}}\]
\[ \Leftrightarrow \frac{2\sqrt{2}\left(\sqrt{3}+1 \right)}{3\sqrt{2+\sqrt{3}}}\]
- Nhân \[ \sqrt{2}\] vào tử và mẫu số, ta có:
\[ \Leftrightarrow \frac{4\left(\sqrt{3}+1 \right)}{3\sqrt{4+2\sqrt{3}}}\]
\[ \Leftrightarrow \frac{4\left(\sqrt{3}+1 \right)}{3\sqrt{3+2\sqrt{3}+1}}\]
\[ \Leftrightarrow \frac{4\left(\sqrt{3}+1 \right)}{3\sqrt{{\left(\sqrt{3}+1 \right)}^{2}}\]
\[ \Leftrightarrow \frac{4\left(\sqrt{3}+1 \right)}{3\left(\sqrt{3}+1 \right)}\]
\[ \Leftrightarrow \frac{4}{3}\].