a: \(A=\frac{\sqrt7+\sqrt3}{\sqrt7-\sqrt3}+\frac{\sqrt7-\sqrt3}{\sqrt7+\sqrt3}\)
\(=\frac{\left(\sqrt7+\sqrt3\right)^2+\left(\sqrt7-\sqrt3\right)^2}{\left(\sqrt7+\sqrt3\right)\left(\sqrt7-\sqrt3\right)}\)
\(=\frac{10+2\sqrt{21}+10-2\sqrt{21}}{7-3}=\frac{20}{4}=5\)
b: \(B=2\sqrt{27}+\sqrt{\left(1-\sqrt3\right)^2}-\frac{4}{\sqrt3+1}\)
\(=2\cdot3\sqrt3+\sqrt3-1-\frac{4\left(\sqrt3-1\right)}{\left(\sqrt3+1\right)\left(\sqrt3-1\right)}\)
\(=7\sqrt3-1-2\left(\sqrt3-1\right)=7\sqrt3-1-2\sqrt3+2=5\sqrt3+1\)
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