[tex] \frac{1}{2 \sqrt{5}- \sqrt{7} }= \frac{2 \sqrt{5}+ \sqrt{7} }{(2 \sqrt{5}- \sqrt{7})(2 \sqrt{5} - \sqrt{7} ) } } = \frac{2 \sqrt{5}+ \sqrt{7} }{ (2 \sqrt{5}) ^{2}- ( \sqrt{7}) ^{2} } = \frac{2 \sqrt{5}+ \sqrt{7} }{20-7}= \frac{2 \sqrt{5}+ \sqrt{7} }{13} [/tex]