helpppppppp: mik cần gấp

$$\text{Lời giải:}$$

Bài `2`:

`a)` `\frac{\sqrt{7}-5}{2} - \frac{6-2\sqrt{7}}{4} + \frac{6}{\sqrt{7}-2} - \frac{5}{4+\sqrt{7}}`

`=\frac{2(\sqrt{7}-5) - (6-2\sqrt{7})}{4}  + \frac{6(\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)}- \frac{5(4-\sqrt{7})}{(4-\sqrt{7})(\sqrt{7}+4)}`

`=\frac{2\sqrt{7}-10 - 6+2\sqrt{7}}{4}  + \frac{6\sqrt{7}+12}{7-4}- \frac{20-5\sqrt{7}}{16-7}`

`= \frac{4\sqrt{7}-16 }{4}  + \frac{6\sqrt{7}+12}{3}- \frac{20-5\sqrt{7}}{9}`

`= \sqrt{7}-4  + 2\sqrt{7}+4- \frac{20-5\sqrt{7}}{9}`

`= 3\sqrt{7}  - \frac{20-5\sqrt{7}}{9}`

`=  \frac{27\sqrt{7}-(20-5\sqrt{7})}{9}`

`=  \frac{32\sqrt{7}-20}{9}`

`------------------`

`b)` `\frac{2}{\sqrt{6}-2} + \frac{2}{\sqrt{6}+2} + \frac{5}{\sqrt{6}}`

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

`= \frac{2\sqrt{6}+4 + 2\sqrt{6}-4}{6-4}+ \frac{5}{\sqrt{6}}`

`= 2\sqrt{6}+ \frac{5}{\sqrt{6}}`

`=  \frac{2.6+5}{\sqrt{6}}`

`=  \frac{17}{\sqrt{6}}`

`----------------`

`c)` `\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}} - \frac{1}{\sqrt{3}+\sqrt{2}+\sqrt{5}}`

`= \frac{\sqrt{3}+\sqrt{2}+\sqrt{5} - (\sqrt{3}+\sqrt{2}-\sqrt{5})   }{(\sqrt{3}+\sqrt{2}-\sqrt{5})(\sqrt{3}+\sqrt{2}+\sqrt{5})}` 

`= \frac{2\sqrt{5} }{(\sqrt{3}+\sqrt{2})^2-(\sqrt{5})^2}` 

`= \frac{2\sqrt{5} }{5 + 2\sqrt{6}-5}` 

`= \frac{2\sqrt{5} }{2\sqrt{6}}` 

`= \frac{\sqrt{5} }{\sqrt{6}}`