`\frac{\sqrt{2+x} + \sqrt{2-x}}{\sqrt{2+x} - \sqrt{2-x}} = \sqrt{2}`

`\frac{(\sqrt{2 + x} + \sqrt{2 - x})^2}{(2 + x) - (2 - x)} = \sqrt{2}`

` \frac{4 + 2\sqrt{(2 + x)(2 - x)}}{(2 + x) - (2 - x) }`

` \frac{4 + 2\sqrt{4 - x^2}}{(2 + x) - (2 - x) }`

`\frac{4 + 2\sqrt{4 - x^2}}{2x} = \sqrt{2}`

`\frac{2 + \sqrt{4 - x^2}}{x} = \sqrt{2}`

`\sqrt{4 - x^2} = x\sqrt{2} - 2`

`2 + \sqrt{4 - x^2} = x\sqrt{2}`

`4 - x^2 = 2x^2 - 4x\sqrt{2} + 4`

`3x^2 - 4x\sqrt{2} = 0`

\(\left[ \begin{array}{1}x=0(L)\\x = \frac{4\sqrt{2}}{3}(N)\end{array} \right.\) 

Thế `x = \frac{4\sqrt{2}}{3}` vào `M`

`M = \frac{\frac{4\sqrt{2}}{3} + 2}{\frac{4\sqrt{2}}{3} - 2}`

` = \frac{4\sqrt{2} + 6}{4\sqrt{2} - 6}`

`= \frac{(4\sqrt{2} + 6)^2}{(4\sqrt{2})^2 - 6^2}`

`= \frac{68 + 48\sqrt{2}}{-4}`

`=M = -17 - 12\sqrt{2}`