\(\dfrac{3\sqrt{2}}{\sqrt{3}+1}=\dfrac{3\sqrt{2}\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=\dfrac{3\sqrt{2}.\sqrt{3}-3\sqrt{2}}{2}=\dfrac{3\sqrt{6}-3\sqrt{2}}{2}\)
\(\dfrac{3\sqrt{2}}{\sqrt{5}+3}=\dfrac{3\sqrt{2}\left(3-\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}=\dfrac{3\sqrt{2}.3-3\sqrt{2}.\sqrt{5}}{9-5}=\dfrac{9\sqrt{2}-3\sqrt{10}}{4}\)
\(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}=\dfrac{\sqrt{3}\left(\sqrt{5}-\sqrt{4}\right)}{\sqrt{5}-2}=\dfrac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}=\sqrt{3}\)
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