\(a,\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
\(=\dfrac{2\sqrt{7}-10-6+2\sqrt{7}}{4}+\dfrac{6\sqrt{7}+12}{3}-\dfrac{20-5\sqrt{7}}{9}\)
\(=\dfrac{4\sqrt{7}-16}{4}+\dfrac{6\sqrt{7}+12}{3}-\dfrac{20-5\sqrt{7}}{9}\)
\(=\sqrt{7}-4+2\sqrt{7}+4-\dfrac{20-5\sqrt{7}}{9}\)
\(=\dfrac{9\sqrt{7}-36+18\sqrt{7}+36-20+5\sqrt{7}}{9}\)
\(=\dfrac{32\sqrt{7}-20}{9}\)
\(b,\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
\(=\dfrac{2\left(\sqrt{6}+2\right)}{2}+\dfrac{2\left(\sqrt{6}-2\right)}{2}+\dfrac{5}{\sqrt{6}}\)
\(=\dfrac{4\sqrt{6}}{2}+\dfrac{5}{\sqrt{6}}\)
\(=\dfrac{17\sqrt{6}}{6}\)
\(c,\dfrac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}-\dfrac{1}{\sqrt{3}+\sqrt{2}+\sqrt{5}}\)
\(=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{3+2+2\sqrt{6}-5}-\dfrac{\sqrt{3}+\sqrt{2}-\sqrt{5}}{3+2+2\sqrt{6}-5}\)
\(=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{3}-\sqrt{2}+\sqrt{5}}{2\sqrt{6}}\)
\(=\dfrac{2\sqrt{5}}{2\sqrt{6}}\)
\(=\dfrac{\sqrt{30}}{6}\)