Đáp án:
`S=1/(\sqrt7+2)`
Giải thích các bước giải:
`A=(\sqrt7-2)/(7+2\sqrt7)`
`B=1/(\sqrt7+2)`
`C=1/\sqrt7`
`⇒S=A-B+C`
`=(\sqrt7-2)/(7+2\sqrt7)-1/(\sqrt7+2)+1/\sqrt7`
`=(\sqrt7-2)/(\sqrt7(\sqrt7+2))-1/(\sqrt7+2)+1/\sqrt7`
`=((\sqrt7-2)+(-\sqrt7)+(\sqrt7+2))/(\sqrt7(\sqrt7+2))`
`=((\sqrt7-\sqrt7+\sqrt7)+(-2+2))/(\sqrt7(\sqrt7+2))`
`=(\sqrt7)/(\sqrt7(\sqrt7+2))`
`=1/(\sqrt7+2)`
Vậy `S=1/(\sqrt7+2)`