Ta có: \(\frac{\sqrt{10}+5\sqrt3}{\sqrt{15}+\sqrt5}-\frac{3}{2\sqrt2-\sqrt5}+\sqrt{9+4\sqrt2}\)
\(=\frac{\sqrt{10}+\sqrt{75}}{\sqrt{15}+\sqrt5}-\frac{3\left(2\sqrt2+\sqrt5\right)}{\left(2\sqrt2-\sqrt5\right)\left(2\sqrt2+\sqrt5\right)}+\sqrt{\left(2\sqrt2+1\right)^2}\)
\(=\frac{\sqrt{15}+\sqrt2}{\sqrt3+1}-\left(2\sqrt2+\sqrt5\right)+2\sqrt2+1\)
\(=\frac{\left(\sqrt{15}+\sqrt2\right)\left(\sqrt3-1\right)}{2}-\sqrt5+1=\frac{3\sqrt5-\sqrt{15}+\sqrt6-\sqrt2-2\sqrt5+2}{2}=\frac{-\sqrt{15}+\sqrt6+\sqrt5-\sqrt2+2}{2}\)
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