$\frac{3\sqrt[]{2} – 2\sqrt[]{3}}{\sqrt[]{3} – \sqrt[]{2}}$ $–$ $\frac{5}{1 – \sqrt[]{6}}$ $+$ $\sqrt[]{24}$

`(3\sqrt{2}-2\sqrt{3})/(\sqrt{3}-\sqrt{2})-(5)/(1-\sqrt{6})+\sqrt{24}`

`=(\sqrt{6}(\sqrt{3}-\sqrt{2}))/(\sqrt{3}-\sqrt{2})-(5(1+\sqrt{6}))/((1-\sqrt{6})(1+\sqrt{6}))+\sqrt{24}`

`=\sqrt{6}-(5(\sqrt{1}+\sqrt{6}))/(-5)+2\sqrt{6}`

`=\sqrt{6}+1+\sqrt{6}+2\sqrt{6}`

`=4\sqrt{6}+1`

Đáp án+Giải thích các bước giải:

 `(3sqrt2-2sqrt3)/(sqrt3-sqrt2)-5/(1-sqrt6)+sqrt24`

`=(sqrt18-sqrt12)/(sqrt3-sqrt2)+(6-1)/(sqrt6-1)+2sqrt6`

`=(sqrt6(sqrt3-sqrt2))/(sqrt3-sqrt2)+((sqrt6-1)(sqrt6+1))/(sqrt6-1)+2sqrt6`

`=sqrt6+sqrt6+1+2sqrt6`

`=4sqrt6+1`