Bài 1: Rút gọn b) √$\frac{3}{2}$ - $\frac{2 √2}{ √3}$ - $\frac{1}{4}$.√$6$ c) $\frac{2}{ √2+ √3}$ + $\frac{3}{ √3- √2}$ d) √$7$-$4 √3$ + √$7+4 √3$ ( dấu √ của cả $4 √3$)

Đáp án + Giải thích các bước giải:

`b)` `\sqrt{3/2}` `-` `(2\sqrt{2})/\sqrt{3}` `-` `1/4` `\sqrt{6}`

`=` `1/2` `\sqrt{6}` `-` `2/3` `\sqrt{6}` `-` `1/4` `\sqrt{6}`

`=` `(1/2-2/3-1/4)` `\sqrt{6}`

`=` `-5/12` `\sqrt{6}`

`c)` `2/(\sqrt{2}+\sqrt{3})` `+` `3/(\sqrt{3}-\sqrt{2})`

`=` `(2(\sqrt{2}-\sqrt{3}))/((\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3}))` `+` `(3(\sqrt{3}+\sqrt{2}))/((\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2}))`

`=` `(2(\sqrt{2}-\sqrt{3}))/(2-3)` `+` `(3(\sqrt{3}+\sqrt{2}))/(3-2)`

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

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

`=` `-2\sqrt{2}` `+` `2\sqrt{3}` `+` `3\sqrt{3}` `+` `3\sqrt{2}`

`=` `\sqrt{2}` `+` `5` `\sqrt{3}`

`d)` `\sqrt{7-4\sqrt{3}}` `+` `\sqrt{7+4\sqrt{3}}`

`=` `\sqrt{(2-\sqrt{3})^2}` `+` `\sqrt{(2+\sqrt{3})^2}`

`=` `|2-\sqrt{3}|` `+` `|2+\sqrt{3}|`

`=` `2` `-` `\sqrt{3}` `+` `2` `+` `\sqrt{3}`

`=` `4`