a: \(5\sqrt{12}+4\sqrt{27}-6\sqrt{48}\)
\(=5\cdot2\sqrt3+4\cdot3\sqrt3-6\cdot4\sqrt3\)
\(=10\sqrt3+12\sqrt3-24\sqrt3=-2\sqrt3\)
b: \(\left(\sqrt{300}-2\sqrt{675}+5\sqrt{75}\right):\sqrt3\)
\(=\frac{10\sqrt3}{\sqrt3}-2\cdot\frac{15\sqrt3}{\sqrt3}+5\cdot\frac{5\sqrt3}{\sqrt3}\)
=10-30+25
=35-30=5
c: \(\cot30^0\cdot\sin^265^0+\tan60^0\cdot\sin^225^0-2\cdot\frac{cos39^0}{\sin51^0}\)
\(=\tan60^0\cdot\sin^265^0+\tan60^0\cdot cos^265^0-2\cdot1\)
\(=\tan60^0-2=\sqrt3-2\)
d: \(\frac{2}{4-2\sqrt3}+\frac{2}{4+2\sqrt3}\)
\(=\frac{2\left(4+2\sqrt3\right)+2\left(4-2\sqrt3\right)}{\left(4+2\sqrt3\right)\left(4-2\sqrt3\right)}\)
\(=\frac{8+4\sqrt3+8-4\sqrt3}{16-12}=\frac{16}{4}=4\)
