Tính: làm chi tiết giúp em `\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}`

Bài này cũng dễ thôi tách `4=2+2=\sqrt4+\sqrt4`

`(sqrt2+sqrt3+sqrt6+sqrt8+4)/(sqrt2+sqrt3+sqrt4)`

`=(sqrt2+sqrt3+sqrt6+sqrt8+2+2)/(sqrt2+sqrt3+sqrt4)`

`=(sqrt2+sqrt3+sqrt4+sqrt4+sqrt6+sqrt8)/(sqrt2+sqrt3+sqrt4)`

`=(sqrt2+sqrt3+sqrt4+sqrt2(sqrt2+sqrt3+sqrt4))/(sqrt2+sqrt3+sqrt4)`

`=((sqrt2+sqrt3+sqrt4)(sqrt2+1))/(sqrt2+sqrt3+sqrt4)`

`=sqrt2+1`