Đáp án + giải thích các bước giải:
12/ `11/(3\sqrt{5}-2\sqrt{3})`
`=(11(3\sqrt{5}+2\sqrt{3}))/(45-12)`
`=(11(3\sqrt{5}+2\sqrt{3}))/33`
`=(3\sqrt{5}+2\sqrt{3})/3`
18/ `(\sqrt{3}+1)/(\sqrt{3}-1)-(\sqrt{3}-1)/(\sqrt{3}+1)`
`=((\sqrt{3}+1)^2-(\sqrt{3}-1)^2)/((\sqrt{3}+1)(\sqrt{3}-1))`
`=(3+2\sqrt{3}+1-3+2\sqrt{3}-1)/(3-1)`
`=(4\sqrt{3})/2`
`=2\sqrt{3}`
19/ `2/\sqrt{8+2\sqrt{15}}-2/\sqrt{8-2\sqrt{15}}`
`=2/\sqrt{5+2.\sqrt{3}.\sqrt{5}+3}-2/\sqrt{5-2.\sqrt{3}.\sqrt{5}+3}`
`=2/\sqrt{(\sqrt{5}+\sqrt{3})^2}-2/\sqrt{(\sqrt{5}-\sqrt{3})^2}`
`=2/|\sqrt{5}+\sqrt{3}|-2/|\sqrt{5}-\sqrt{3}|`
`=2/(\sqrt{5}+\sqrt{3})-2/(\sqrt{5}-\sqrt{3})`
`=(2(\sqrt{5}-\sqrt{3})-2(\sqrt{5}+\sqrt{3}))/((\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3}))`
`=(2\sqrt{5}-2\sqrt{3}-2\sqrt{5}-2\sqrt{3})/(5-3)`
`=(-4\sqrt{3})/2`
`=-2\sqrt{3}`
21/ `(2+\sqrt{3})/\sqrt{(\sqrt{3}-2)^2}-(2-\sqrt{3})/\sqrt{7+4\sqrt{3}}`
`=(2+\sqrt{3})/|\sqrt{3}-2|-(2-\sqrt{3})/\sqrt{4+2.2.\sqrt{3}+3}`
`=(2+\sqrt{3})/(2-\sqrt{3})-(2-\sqrt{3})/\sqrt{(2+\sqrt{3})^2}`
`=(2+\sqrt{3})/(2-\sqrt{3})-(2-\sqrt{3})/|2+\sqrt{3}|`
`=(2+\sqrt{3})/(2-\sqrt{3})-(2-\sqrt{3})/(2+\sqrt{3})`
`=((2+\sqrt{3})^2-(2-\sqrt{3})^2)/((2-\sqrt{3})(2+\sqrt{3}))`
`=(4+4\sqrt{3}+3-4+4\sqrt{3}-3)/(4-3)`
`=8\sqrt{3}`
