`a)A=1/[1+\sqrt{2}]+1/[\sqrt{2}+\sqrt{3}]-2/[\sqrt{3}+1]`
`A=[1-\sqrt{2}]/[1-2]+[\sqrt{2}-\sqrt{3}]/[2-3]-[2(\sqrt{3}+1)]/[3-1]`
`A=\sqrt{2}-1+\sqrt{3}-\sqrt{2}-\sqrt{3}-1=-2`
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`b)B=[\sqrt{125}+1]/[\sqrt{5}+1]-[\sqrt{8}-1]/[\sqrt{2}-1]+3/[\sqrt{5}-\sqrt{2}]`
`B=[(\sqrt{5}+1)(5-\sqrt{5}+1)]/[\sqrt{5}+1]-[(\sqrt{2}-1)(2+\sqrt{2}+1)]/[\sqrt{2}-1]+[3(\sqrt{5}+\sqrt{2})]/[5-2]`
`B=5-\sqrt{5}+1-2-\sqrt{2}-1+\sqrt{5}+\sqrt{2}=3`
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`c)C=\sqrt{8-2\sqrt{15}}+\sqrt{5-2\sqrt{6}}+\sqrt{3+2\sqrt{2}}`
`C=\sqrt{(\sqrt{5}-\sqrt{3})^2}+\sqrt{(\sqrt{3}-\sqrt{2})^2}+\sqrt{(\sqrt{2}+1)^2}`
`C=\sqrt{5}-\sqrt{3}+\sqrt{3}-\sqrt{2}+\sqrt{2}+1
`C=\sqrt{5}+1`
\(a,A=\dfrac{1-\sqrt{2}}{1-2}+\dfrac{\sqrt{2}-\sqrt{3}}{2-3}-\dfrac{2\left(\sqrt{3}-1\right)}{3-1}\\ =\sqrt{2}+1+\sqrt{3}-\sqrt{2}-\sqrt{3}+1\\ =2\\ \)
