Đáp án+Giải thích các bước giải:

 `1)\frac{6-\sqrt{6}}{\sqrt{6}-1}+\frac{6-\sqrt{6}}{\sqrt{6}}`

`=\frac{\sqrt{6}.(\sqrt{6}-1)}{\sqrt{6}-1}+\frac{\sqrt{6}.(\sqrt{6}-1)}{\sqrt{6}}`

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

`=2\sqrt{6}-1`

`2)\frac{6-6\sqrt{3}}{1-\sqrt{3}}+\frac{3+\sqrt{3}}{\sqrt{3}+1}`

`=\frac{6.(1-\sqrt{3})}{1-\sqrt{3}}+\frac{\sqrt{3}.(\sqrt{3}+1)}{\sqrt{3}+1}`

`=6+\sqrt{3}`

`3)\frac{3+\sqrt{3}}{\sqrt{3}}+\frac{\sqrt{6}-\sqrt{3}}{1-\sqrt{2}}`

`=\frac{\sqrt{3}.(\sqrt{3}+1)}{\sqrt{3}}-\frac{\sqrt{3}.(\sqrt{2}-1)}{\sqrt{2}-1}`

`=\sqrt{3}+1-\sqrt{3}`

`=1`

`4)\frac{2-\sqrt{2}}{1-\sqrt{2}}+\frac{\sqrt{2}-\sqrt{6}}{\sqrt{3}-1}`

`=\frac{\sqrt{2}.(\sqrt{2}-1)}{-(\sqrt{2}-1)}+\frac{-\sqrt{2}.(\sqrt{3}-1)}{\sqrt{3}-1}`

`=-\sqrt{2}-\sqrt{2}`

`=-2\sqrt{2}`