we need to rationalize the denomenator
remember
(a+b)(a-b)=a²-b²
the bottom is the (a+b) form
mutliply it by [tex] \frac{ \sqrt{2}- \sqrt{10} }{\sqrt{2}- \sqrt{10}} [/tex]
[tex] (\frac{ \sqrt{2}- \sqrt{10} }{\sqrt{2}+ \sqrt{10}})(\frac{ \sqrt{2}- \sqrt{10} }{\sqrt{2}- \sqrt{10}}) [/tex]=
[tex] \frac{ (\sqrt{2}- \sqrt{10})^2 }{(\sqrt{2})^2- (\sqrt{10})^2} [/tex]=
[tex] \frac{ 12-4\sqrt{5} }{2-10} [/tex]=
[tex] \frac{ 12-4\sqrt{5} }{-8} [/tex]=
[tex] \frac{ \sqrt{5}-3 }{2} [/tex]
