Đáp án+Giải thích các bước giải:

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

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

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

`=(2.4)/(4-3)`

`=(2.4)/(1)`

`=8`

`b)(2)/(\sqrt{5}-\sqrt{3})+(2)/(\sqrt{7}-\sqrt{5})`

`=(2.(\sqrt{5}+\sqrt{3}))/((\sqrt{5}-\sqrt{3}).(\sqrt{5}+\sqrt{3}))+(2.(\sqrt{7}+\sqrt{5}))/((\sqrt{7}-\sqrt{5}).(\sqrt{7}+\sqrt{5}))`

`=(2.(\sqrt{5}+\sqrt{3}))/((\sqrt{5})^{2}-(\sqrt{3})^{2})+(2.(\sqrt{7}+\sqrt{5}))/((\sqrt{7})^{2}-(\sqrt{5})^{2})`

`=(2.(\sqrt{5}+\sqrt{3}))/(2)+(2.(\sqrt{7}+\sqrt{5}))/(2)`

`=\sqrt{5}+\sqrt{3}+\sqrt{7}+\sqrt{5}`

`=\sqrt{3}+\sqrt{7}+2\sqrt{5}`

`c)(\sqrt{14}-\sqrt{7})/(\sqrt{2}-1)+(\sqrt{6}-2)/(\sqrt{3}-\sqrt{2})`

`=(\sqrt{7}.(\sqrt{2}-1))/(\sqrt{2}-1)+(\sqrt{2}.\sqrt{3}-(\sqrt{2})^{2})/(\sqrt{3}-\sqrt{2})`

`=\sqrt{7}+(\sqrt{2}.(\sqrt{3}-\sqrt{2}))/(\sqrt{3}-\sqrt{2})`

`=\sqrt{7}+\sqrt{2}`