6:
a: \(=\dfrac{20\cdot2\sqrt{3}-15\cdot3\sqrt{3}}{5\sqrt{3}}=\dfrac{40\sqrt{3}-45\sqrt{3}}{5\sqrt{3}}\)
\(=-\dfrac{5\sqrt{3}}{5\sqrt{3}}=-1\)
b: \(=\dfrac{5\sqrt{3}+9\sqrt{3}-4\sqrt{3}}{\sqrt{3}}=5+9-4=10\)
c: \(\left(\sqrt{2}+1\right)^2+\left(\sqrt{2}-1\right)^2\)
\(=3+2\sqrt{2}+3-2\sqrt{2}\)
=6
d: \(=\left(2\sqrt{7}-2\sqrt{3}+\sqrt{7}\right)\cdot\sqrt{7}+2\sqrt{21}\)
\(=\left(3\sqrt{7}-2\sqrt{3}\right)\cdot\sqrt{7}+2\sqrt{21}\)
\(=21-2\sqrt{21}+2\sqrt{21}=21\)