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1). [tex] \frac{3}{ \sqrt{5} }= \frac{3}{ \sqrt{5}}* \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{3 \sqrt{5} }{5} [/tex]
2). [tex] \frac{4}{\sqrt{5}+\sqrt{3}}=\frac{4}{\sqrt{5}+\sqrt{3}}* \frac{ \sqrt{5}- \sqrt{3} }{\sqrt{5}-\sqrt{3}}= \frac{4(\sqrt{5}-\sqrt{3})}{5-3}=2(\sqrt{5}-\sqrt{3})[/tex]
3). [tex] \frac{6(3+\sqrt{5})(3-\sqrt{5})}{2-\sqrt{6}} = \frac{6(9-5)}{2-\sqrt{6}}= \frac{24}{2- \sqrt{6}}= \frac{24}{2-\sqrt{6}}* \frac{2+ \sqrt{6}}{2+\sqrt{6}}= \frac{24(2+\sqrt{6}}{4-6}[/tex] = [tex]-12(2+ \sqrt{6})=-24-12 \sqrt{6} [/tex]