[tex] \frac{3 \sqrt{5}+ \sqrt{3} }{ \sqrt{5}- \sqrt{3} } = \frac{(3 \sqrt{5}+ \sqrt{3})( \sqrt{5}+ \sqrt{3} ) }{ (\sqrt{5}- \sqrt{3})( \sqrt{5}+ \sqrt{3} ) }= \frac{15+3 \sqrt{15}+ \sqrt{15}+3 }{5-3 }=\frac{18+4 \sqrt{15} }{2 }= \\\\ =\frac{2(9+2 \sqrt{15}) }{2 }=9+2 \sqrt{15} [/tex]
