a: \(=\dfrac{2\sqrt{7}-10-6+2\sqrt{7}}{4}+4+2\sqrt{7}-\dfrac{20-5\sqrt{7}}{9}\)
\(=\sqrt{7}-4+4+2\sqrt{7}-\dfrac{20-5\sqrt{7}}{9}\)
\(=\dfrac{27\sqrt{7}-20+5\sqrt{7}}{9}=\dfrac{32\sqrt{7}-20}{9}\)
b: \(=2+\sqrt{6}-2+\sqrt{6}+\dfrac{5}{\sqrt{6}}\)
\(=2\sqrt{6}+\dfrac{5}{\sqrt{6}}=\dfrac{17}{\sqrt{6}}\)
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a, \(=\dfrac{2\sqrt{7}-10-6+2\sqrt{7}}{4}-\dfrac{6\left(\sqrt{7}-2\right)}{3}-\dfrac{5\left(4-\sqrt{7}\right)}{9}\)
\(=\sqrt{7}-4-2\left(\sqrt{7}-2\right)-\dfrac{20-5\sqrt{7}}{9}\)
\(=\dfrac{-9\sqrt{7}-20+5\sqrt{7}}{9}=\dfrac{-4\sqrt{7}-20}{9}\)
b, \(=\dfrac{2\sqrt{6}+4+2\sqrt{6}-4}{2}+\dfrac{5\sqrt{6}}{6}=2\sqrt{6}+\dfrac{5\sqrt{6}}{6}=\dfrac{23\sqrt{6}}{6}\)
c, \(=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{3}-\sqrt{2}+\sqrt{5}}{\left(\sqrt{3}+\sqrt{2}\right)^2-5}=\dfrac{2\sqrt{5}}{2\sqrt{6}}=\dfrac{\sqrt{30}}{6}\)
