Đáp án:
$-1$
Giải thích các bước giải:
$\frac{8 + 2\sqrt{2}}{3 - \sqrt{2}}- \frac{2 + 3\sqrt{2}}{\sqrt{2}}+ \frac{\sqrt{2}}{1 - \sqrt{2} }$
$= \frac{(8 + 2\sqrt{2})(3 + \sqrt{2})}{(3 - \sqrt{2})(3+\sqrt{2})}- \frac{\sqrt{2}(\sqrt{2}+3)}{\sqrt{2}}+ \frac{\sqrt{2}(1 + \sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}$
$= \frac{28 + 14\sqrt{2}}{7}- (\sqrt{2}+3)+ \frac{\sqrt{2}(1 + \sqrt{2})}{-1}$
$= \frac{14(2+ \sqrt{2})}{7}- \sqrt{2} - 3- \sqrt{2}(1+ \sqrt{2})$
$= 2(2 + \sqrt{2})- \sqrt{2} - 3 - \sqrt{2}-2$
$= 4 + 2\sqrt{2} - 2\sqrt{2} - 5$
$= -1$