10:
\(=\dfrac{\left(\sqrt{2}-\sqrt{3}\right)}{\sqrt{2}+\sqrt{3}}+\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{2}-\sqrt{3}}\)
\(=\dfrac{\left(\sqrt{2}-\sqrt{3}\right)^2+\left(\sqrt{2}+\sqrt{3}\right)^2}{2-3}\)
\(=\dfrac{5-2\sqrt{6}+5+2\sqrt{6}}{-1}=-10\)
11: \(=\dfrac{\left(\sqrt{2}-1\right)\left(3+\sqrt{2}\right)-\left(3-\sqrt{2}\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}+1\right)\left(3+\sqrt{2}\right)}\)
\(=\dfrac{3\sqrt{2}+2-3-\sqrt{2}-3\sqrt{2}-3+2+\sqrt{2}}{\left(\sqrt{2}+1\right)\left(3+\sqrt{2}\right)}\)
\(=\dfrac{-2}{\left(\sqrt{2}+1\right)\left(3+\sqrt{2}\right)}=\dfrac{10-8\sqrt{2}}{7}\)
12:
\(=\dfrac{\left(\sqrt{5}+2\right)^2}{5-4}-\dfrac{\left(6-2\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}\)
\(=9+4\sqrt{5}-\dfrac{2\left(3-\sqrt{5}\right)^2}{4}\)
\(=\dfrac{36+16\sqrt{5}-2\left(14-6\sqrt{5}\right)}{4}\)
\(=\dfrac{8+28\sqrt{5}}{4}=7\sqrt{5}+2\)
