Question

\(（\frac{1-\sqrt{2}}{1+\sqrt{2}}-\frac{1+\sqrt{2}}{1-\sqrt{2}}）：\sqrt{72}\)

Answer 1

\(\left(\frac{1-\sqrt{2}}{1+\sqrt{2}}-\frac{1+\sqrt{2}}{1-\sqrt{2}}\right):\sqrt{72}\)

\(\left[\frac{\left(1-\sqrt{2}\right)^2-\left(1+\sqrt{2}\right)^2}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}\right]:\sqrt{72}\)

\(=\frac{1-2\sqrt{2}+2-1-2\sqrt{2}-2}{1-2}\cdot\frac{1}{\sqrt{72}}\)

\(=\frac{-2\sqrt{2}-2\sqrt{2}}{-1}\cdot\frac{1}{\sqrt{72}}\)

\(=4\sqrt{2}\cdot\frac{1}{2\sqrt{18}}=\frac{2}{\sqrt{9}}=\frac{2}{3}\)