\(1,\\ a,=2\sqrt{5}-4\sqrt{2}+6\sqrt{2}-12\sqrt{2}=-10\sqrt{2}+2\sqrt{5}\\ b,=4\sqrt{6a}-3\sqrt{6a}+3\sqrt{6a}-\dfrac{1}{2}\cdot5\sqrt{6a}=\dfrac{3}{2}\sqrt{6a}\\ c,=21+4\sqrt{21}-2\sqrt{21}=21+2\sqrt{21}\\ d,=\left(6\sqrt{7}+\sqrt{7}-2\sqrt{2}\right)\cdot\sqrt{7}+2\sqrt{14}\\ =\left(7\sqrt{7}-2\sqrt{2}\right)\sqrt{7}+2\sqrt{14}\\ =49-2\sqrt{14}+2\sqrt{14}=49\)
\(2,\\ a,=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}=\dfrac{6}{7}\\ b,=\dfrac{6\sqrt{2}+8-6\sqrt{2}+8}{\left(3\sqrt{2}-4\right)\left(3\sqrt{2}+4\right)}=\dfrac{16}{2}=8\\ c,=\dfrac{\sqrt{15}}{5}+\dfrac{\sqrt{15}}{30}-\dfrac{\sqrt{15}}{15}\\ =\dfrac{6\sqrt{15}+\sqrt{15}-2\sqrt{15}}{30}=\dfrac{5\sqrt{15}}{30}=\dfrac{\sqrt{15}}{6}\\ d,=\dfrac{15\left(\sqrt{6}+1\right)}{6-1}+\dfrac{4\left(\sqrt{6}+2\right)}{6-4}-\dfrac{12\left(3+\sqrt{6}\right)}{9-6}-\sqrt{6}\\ =3\left(\sqrt{6}+1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)-\sqrt{6}\\ =3\sqrt{6}+3+2\sqrt{6}+4-12-4\sqrt{6}-\sqrt{6}=\sqrt{6}-5\)
