\(1,\dfrac{\sqrt{6}\left(\sqrt{6}-1\right)}{\sqrt{6}-1}+\dfrac{\sqrt{6}\left(\sqrt{6}+1\right)}{\sqrt{6}}=\sqrt{6}+\sqrt{6}+1=2\sqrt{6}+1\)
\(2,\dfrac{6\left(1-\sqrt{3}\right)}{1-\sqrt{3}}+\dfrac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}=6+3=9\)
\(3,\dfrac{\sqrt{3}\left(\sqrt{3}+1\right)}{\sqrt{3}}-\dfrac{\sqrt{3}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}=\sqrt{3}-\sqrt{3}=0\)
\(4,\dfrac{\sqrt{2}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}+\dfrac{\sqrt{2}\left(1-\sqrt{3}\right)}{\sqrt{3}-1}=\sqrt{2}-\sqrt{2}=0\)
\(5,\dfrac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\dfrac{\sqrt{2}\left(1-\sqrt{2}\right)}{\sqrt{2}-1}=\sqrt{2}-\sqrt{2}=0\)
\(6,\dfrac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\dfrac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}=\sqrt{5}+\dfrac{\sqrt{5}}{2}=\dfrac{2\sqrt{5}+\sqrt{5}}{2}=\dfrac{3\sqrt{5}}{2}\)
1) \(\dfrac{6-\sqrt{6}}{\sqrt{6}-1}+\dfrac{6+\sqrt{6}}{\sqrt{6}}\)
\(=\dfrac{\sqrt{6}\left(\sqrt{6}-1\right)}{\sqrt{6}-1}+\dfrac{\sqrt{6}\left(\sqrt{6}+1\right)}{\sqrt{6}}\)
\(=\sqrt{6}+\sqrt{6}+1\)
\(=2\sqrt{6}+1\)
2) \(\dfrac{6-6\sqrt{3}}{1-\sqrt{3}}+\dfrac{3\sqrt{3}+3}{\sqrt{3}+1}\)
\(=\dfrac{6\left(1-\sqrt{3}\right)}{1-\sqrt{3}}+\dfrac{3\left(\sqrt{3}+1\right)}{\sqrt{3}+1}\)
\(=6+3\)
\(=9\)
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