1.
$$
\frac{3 \sqrt{15}-\sqrt{10}-2 \sqrt{6}+3 \sqrt{3}-\sqrt{2}+18}{\sqrt{5}+2 \sqrt{3}+1}
$$
$=$
$\begin{array}{l}=1 .3 \sqrt{3}-\sqrt{2} \text {. } \\ \text { Solution 1: Expression }=\frac{3 \sqrt{3} \cdot \sqrt{5}-\sqrt{2} \cdot \sqrt{5}-2 \sqrt{2} \cdot \sqrt{3}+3 \sqrt{3}-\sqrt{2}+3 \sqrt{3} \cdot 2 \sqrt{3}}{\sqrt{5}+2 \sqrt{3}+1} \\ =\frac{3 \sqrt{3}(\sqrt{5}+2 \sqrt{3}+1)-\sqrt{2}(\sqrt{5}+2 \sqrt{3}+1)}{\sqrt{5}+2 \sqrt{3}+1}=3 \sqrt{3}-\sqrt{2} \text {. } \\ \text { Solution 2: Original expression }=\frac{\sqrt{5}(3 \sqrt{3}-\sqrt{2})+2 \sqrt{3}(3 \sqrt{3}-\sqrt{2})+(3 \sqrt{3}-\sqrt{2})}{\sqrt{5}+2 \sqrt{3}+1} \\ =3 \sqrt{3}-\sqrt{2} . \\\end{array}$