Đáp án:
`(1/(sqrt{5}-sqrt{3})-1/(sqrt{5}+sqrt{3})):(2-sqrt{3})/(sqrt{3}+2)=12+7sqrt{3}`
Giải thích các bước giải:
`b)`
`(1/(sqrt{5}-sqrt{3})-1/(sqrt{5}+sqrt{3})):(2-sqrt{3})/(sqrt{3}+2)`
`=((sqrt{5}+sqrt{3})/((sqrt{5}-sqrt{3})(sqrt{5}+sqrt{3}))-(sqrt{5}-sqrt{3})/((sqrt{5}+sqrt{3})(sqrt{5}-sqrt{3}))). (sqrt{3}+2)/(2-sqrt{3})`
`=((sqrt{5}+sqrt{3})/(5-3)-(sqrt{5}-sqrt{3})/(5-3)) . (sqrt{3}+2)/(2-sqrt{3})`
`=(sqrt{5}+sqrt{3}-sqrt{5}+sqrt{3})/2 . (sqrt{3}+2)/(2-sqrt{3})`
`=(2sqrt{3})/2 . (sqrt{3}+2)/(2-sqrt{3})`
`=sqrt{3}.(sqrt{3}+2)/(2-sqrt{3})`
`=(sqrt{3}.(sqrt{3}+2))/(2-sqrt{3})`
`=(3+2sqrt{3})/(2-sqrt{3})`
`=((3+2sqrt{3})(2+sqrt{3}))/((2-sqrt{3})(2+sqrt{3}))`
`=(6+3sqrt{3}+4sqrt{3}+6)/1`
`=12+7sqrt{3}`
