[tex] \frac{ \sqrt{3}- \sqrt{6} }{\sqrt{3}+\sqrt{6}} = \frac{ (\sqrt{3}- \sqrt{6})(\sqrt{3}- \sqrt{6}) }{(\sqrt{3}+\sqrt{6})(\sqrt{3}- \sqrt{6})} = \frac{(\sqrt{3}- \sqrt{6})^2}{3-6}= \frac{3-2 \sqrt{18}+6 }{-3} = \frac{9-6 \sqrt{2} }{-3}= \\ \\ = \frac{3(3-2 \sqrt{2}) }{-3}= \frac{(3-2 \sqrt{2}) }{-1}=-(3-2 \sqrt{2} )=-3+2 \sqrt{2} [/tex]
Hope this helps
