[tex]\dfrac{\sqrt3}{\sqrt5+\sqrt3}\cdot\dfrac{\sqrt5-\sqrt3}{\sqrt5-\sqrt3}=\dfrac{\sqrt{15}-\sqrt{3^2}}{(\sqrt5)^2-(\sqrt3)^2}=\dfrac{\sqrt{15}-3}{5-3}=\boxed{\dfrac{\sqrt{15}-3}{2}}\\[/tex]
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[tex]\dfrac{\sqrt3}{\sqrt5+\sqrt3}\cdot\dfrac{\sqrt5-\sqrt3}{\sqrt5-\sqrt3}=\dfrac{\sqrt{15}-\sqrt{3^2}}{(\sqrt5)^2-(\sqrt3)^2}=\dfrac{\sqrt{15}-3}{5-3}=\boxed{\dfrac{\sqrt{15}-3}{2}}\\[/tex]