a)\(\dfrac{15}{\sqrt{16}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}-\sqrt{6}\)
=\(3+\dfrac{4}{\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)}-\dfrac{12}{\sqrt{3}\left(\sqrt{3}-\sqrt{2}\right)}-\sqrt{6}\)
=\(3+\dfrac{2\sqrt{2}-4\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\sqrt{6}=\dfrac{3\left(\sqrt{3}-\sqrt{2}\right)+2\sqrt{2}-4\sqrt{3}-\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}\)
=\(\dfrac{3\sqrt{3}-3\sqrt{2}+2\sqrt{2}-4\sqrt{3}-3\sqrt{2}+2\sqrt{3}}{\sqrt{3}-\sqrt{2}}\)
=\(\dfrac{\sqrt{3}-4\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)
b)\(\dfrac{\sqrt{2}-1}{\sqrt{2}+2}-\dfrac{2}{2+\sqrt{2}}+\dfrac{\sqrt{2}+1}{\sqrt{2}}\)=\(\dfrac{\sqrt{2}-1-2+\left(\sqrt{2}+1\right)^2}{\sqrt{2}\left(\sqrt{2}+1\right)}\)
=\(\dfrac{\sqrt{2}-1-2+2+2\sqrt{2}+1}{\sqrt{2}\left(\sqrt{2}+1\right)}=\dfrac{3\sqrt{2}}{\sqrt{2}\left(\sqrt{2}+1\right)}=\dfrac{3}{\sqrt{2}+1}\)
