rút gọn biểu thức: (3+ √2)/(2 √2 – 1) – √ [(1+ √2)/( √2-1)]

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1. $\dfrac{3+\sqrt[]{2}}{2\sqrt[]{2}-1}-\sqrt[]{\dfrac{1+\sqrt[]{2}}{\sqrt[]{2}-1}}$

   $=\dfrac{3+\sqrt[]{2}}{2\sqrt[]{2}-1}-\sqrt[]{\dfrac{(1+\sqrt[]{2})(\sqrt[]{2}+1)}{(\sqrt[]{2}-1)(\sqrt[]{2}+1)}}$

   $=\dfrac{3+\sqrt[]{2}}{2\sqrt[]{2}-1}-\sqrt[]{(\sqrt[]{2}+1)^2}$

   $=\dfrac{3+\sqrt[]{2}}{2\sqrt[]{2}-1}-|\sqrt[]{2}+1|$

   $=\dfrac{3+\sqrt[]{2}}{2\sqrt[]{2}-1}-(\sqrt[]{2}+1)$

   $=\dfrac{3+\sqrt[]{2}-(2\sqrt[]{2}-1)(\sqrt[]{2}+1)}{2\sqrt[]{2}-1}$

   $=\dfrac{3+\sqrt[]{2}-(3+\sqrt[]{2})}{2\sqrt[]{2}-1}$

   $=0$

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