Đáp án:
`=(9\sqrt{5}+10\sqrt{6}-15\sqrt{7}+\sqrt{210})/13`
Giải thích các bước giải:
`(2\sqrt{30})/(\sqrt{5}+\sqrt{6}+\sqrt{7})`
`=(2\sqrt{30}(\sqrt{5}+\sqrt{6}-\sqrt{7}))/((\sqrt{5}+\sqrt{6})^2-\sqrt{7}^2)`
`=(2\sqrt{30}(\sqrt{5}+\sqrt{6}-\sqrt{7}))/(5+6+2\sqrt{30}-7)`
`=(2\sqrt{30}(\sqrt{5}+\sqrt{6}-\sqrt{7}))/(4+2\sqrt{30})`
`=(2\sqrt{30}(2\sqrt{30}-4)(\sqrt{5}+\sqrt{6}-\sqrt{7}))/(4.30-16)`
`=(2\sqrt{30}(2\sqrt{30}-4)(\sqrt{5}+\sqrt{6}-\sqrt{7}))/(120-16)`
`=(2\sqrt{30}(2\sqrt{30}-4)(\sqrt{5}+\sqrt{6}-\sqrt{7}))/(104)`
`=(\sqrt{30}(\sqrt{30}-2)(\sqrt{5}+\sqrt{6}-\sqrt{7}))/26`
`=((30-2\sqrt{30})(\sqrt{5}+\sqrt{6}-\sqrt{7}))/26`
`=((15-\sqrt{30})(\sqrt{5}+\sqrt{6}-\sqrt{7}))/13`
`=(15\sqrt{5}+15\sqrt{6}-15\sqrt{7}-5\sqrt{6}-6\sqrt{5}+\sqrt{210})/13`
`=(9\sqrt{5}+10\sqrt{6}-15\sqrt{7}+\sqrt{210})/13`
