a)A=\(\frac{\sqrt3}{\sqrt{\sqrt3+1}-1}-\frac{\sqrt3}{\sqrt{\sqrt3+1}+1}\)

A=\(\frac{\sqrt3*(\sqrt{\sqrt3+1}+1)}{\left(\sqrt{\sqrt3+1}-1\right)*\left(\sqrt{\sqrt3+1}+1\right)}-\frac{\sqrt3*(\sqrt{\sqrt3+1}-1)}{\left(\sqrt{\sqrt3+1}-1\right)*\left(\sqrt{\sqrt3+1}+1\right)}\)

A=\(\frac{\sqrt3\times(\sqrt{\sqrt3+1}+1)-\sqrt3\times(\sqrt{\sqrt3+1}-1)}{\left(\sqrt{\sqrt3+1}-1\right)*\left(\sqrt{\sqrt3+1}+1\right)}\)

\(A=\frac{2\sqrt3}{\sqrt3}\)

A=2

b) \(B = \left(\right. \frac{15}{\sqrt{6} + 1} + \frac{4}{\sqrt{6} - 2} - \frac{12}{3 - \sqrt{6}} \left.\right) \left(\right. \sqrt{6} + 11 \left.\right)\)

B=\((3\sqrt6-3+2\sqrt6+4-12-4\sqrt6)\times(\sqrt6+1)\)

=\((\sqrt6-11)\times(\sqrt6+1)\)

=\(6+\sqrt6-11\sqrt6-11\)

=\(-5-10\sqrt6\)

c)C\(= 4 \sqrt{20} - 3 \sqrt{125} + 5 \sqrt{45} - 15 \sqrt{\frac{1}{5}}\).

=\(4\times2\sqrt5-3\times5\sqrt5+5\times3\sqrt5-3\sqrt5\)

=\(8\sqrt5-15\sqrt5+15\sqrt5-3\sqrt5\)

=\(5\sqrt5\)