a, \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(2+\sqrt{3}\right)\)
\(=\frac{\left(3+2\sqrt{3}\right).\sqrt{3}}{3}+\frac{\left(2+\sqrt{2}\right).\left(\sqrt{2}-1\right)}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}-\left(2+\sqrt{3}\right)\)
\(=\frac{3\sqrt{3}+6}{3}+\frac{2\sqrt{2}-2+2-\sqrt{2}}{2-1}-2-\sqrt{3}\)
\(=\frac{3\sqrt{3}+6}{3}+\sqrt{2}-2-\sqrt{3}\)
\(=\frac{3\sqrt{3}+6+3\left(\sqrt{2}-2-\sqrt{3}\right)}{3}\)
\(=\frac{3\sqrt{3}+6+3\sqrt{2}-6-3\sqrt{3}}{3}\)
\(=\frac{3\sqrt{2}}{3}=\sqrt{2}\)
b, \(\sqrt{6-2\sqrt{5}}+\sqrt{8+2\sqrt{15}}-2\sqrt{3}\)
\(=\sqrt{\left(\sqrt{5}-1\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-2\sqrt{3}\)
\(=\left|\sqrt{5}-1\right|+\left|\sqrt{5}+\sqrt{3}\right|-2\sqrt{3}\)
\(=\sqrt{5}-1+\sqrt{5}+\sqrt{3}-2\sqrt{3}\) (vì \(\sqrt{5}-1>0,\sqrt{5}+\sqrt{3}>0\))
\(=2\sqrt{5}-\sqrt{3}-1\)
\(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}}-\left(2+\sqrt{3}\right)\)
=\(\frac{\sqrt{3}\left(\sqrt{3}+2\right)}{\sqrt{3}}+\frac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}-2-\sqrt{3}\)
\(=\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}\)
=\(\sqrt{2}\)
