[tex] \frac{1}{ \sqrt{2} }- \frac{1}{ \sqrt{2}- \sqrt{5}} = \frac{ \sqrt{2} }{2}- \frac{ \sqrt{2}+ \sqrt{5} }{2-5}= \frac{ \sqrt{2} }{2}- \frac{ \sqrt{2}+ \sqrt{5} }{-3}= \frac{ \sqrt{2} }{2}+ \frac{ \sqrt{2}+ \sqrt{5} }{3}= \\ = \frac{3 \sqrt{2} }{6}+ \frac{2 \sqrt{2} +2 \sqrt{5} }{6} = \boxed{\frac{5 \sqrt{2}+2 \sqrt{5} }{6}}. [/tex]
