Đáp án:
`{13}/2+1/6\sqrt{3}`
Giải thích các bước giải:
`16)` `3/{2-\sqrt{3}}+5/{3+\sqrt{3}}-4/{\sqrt{3}-1}`
`={3(2+\sqrt{3})}/{(2-\sqrt{3})(2+\sqrt{3})}+{5(3-\sqrt{3})}/{(3+\sqrt{3})(3-\sqrt{3})}-{4(\sqrt{3}+1)}/{(\sqrt{3}-1)(\sqrt{3}+1)}`
`={6+3\sqrt{3}}/{2^2-3}+{15-5\sqrt{3}}/{3^2-3}-{4(\sqrt{3}+1)}/{3-1^2}`
`=6+3\sqrt{3}+{15-5\sqrt{3}}/6-2(\sqrt{3}+1)`
`=6+3\sqrt{3}+{15}/6-5/6\sqrt{3}-2\sqrt{3}-2`
`=(6+{15}/6-2)+(3\sqrt{3}-5/6\sqrt{3}-2\sqrt{3})`
`={13}/2+1/6\sqrt{3}`
Vậy: `3/{2-\sqrt{3}}+5/{3+\sqrt{3}}-4/{\sqrt{3}-1}`
`={13}/2+1/6\sqrt{3}`