`a)[\sqrt{15}+\sqrt{3}]/[\sqrt{10}+\sqrt{2}]`
`=[\sqrt{3}(\sqrt{5}+1)]/[\sqrt{2}(\sqrt{5}+1)]`
`=\sqrt{3}/\sqrt{2}=\sqrt{6}/2`
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`b)1/[\sqrt{2}+\sqrt{5}]+1/[\sqrt{2}-\sqrt{5}]`
`=[\sqrt{2}-\sqrt{5}+\sqrt{2}+\sqrt{5}]/[(\sqrt{2}+\sqrt{5})(\sqrt{2}-\sqrt{5})]`
`=[2\sqrt{2}]/[2-5]`
`=[-2\sqrt{2}]/3`
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`c)[(\sqrt{5}+2)^2-8\sqrt{5}]/[\sqrt{5}-2]`
`=[5+4\sqrt{5}+4-8\sqrt{5}]/[\sqrt{5}-2]`
`=[5-4\sqrt{5}+4]/[\sqrt{5}-2]`
`=[(\sqrt{5}-2)^2]/[\sqrt{5}-2]=\sqrt{5}-2`
Bài 5
\(a,=\dfrac{\sqrt{3}\left(\sqrt{5}+1\right)}{\sqrt{2}\left(\sqrt{5}+1\right)}\\ =\dfrac{\sqrt{3}}{\sqrt{2}}\\ =\dfrac{\sqrt{6}}{2}\\ b,=\dfrac{\sqrt{2}-\sqrt{5}+\sqrt{2}+\sqrt{5}}{2-5}\\ =\dfrac{2\sqrt{2}}{-3}\\ =\dfrac{-2\sqrt{2}}{3}\\ c,=\dfrac{9+4\sqrt{5}-8\sqrt{5}}{\sqrt{5}-2}\\ =\dfrac{9-4\sqrt{5}}{\sqrt{5}-2}\\ =\dfrac{\left(\sqrt{5}-2\right)^2}{\sqrt{5}-2}=\sqrt{5}-2\)