Question

(raiz de 5 menos 1)/ (raiz de 3 menos raiz de 5)

Answer 1

$\frac{ \sqrt{5}-1 }{ \sqrt{3}- \sqrt{5} } =\frac{ (\sqrt{5}-1) .( \sqrt{3}+ \sqrt{5} ) }{( \sqrt{3}- \sqrt{5} ) .( \sqrt{3}+ \sqrt{5} ) }= \frac{ \sqrt{5} . \sqrt{3} + ( \sqrt{5} )^{2}- \sqrt{3} - \sqrt{5} }{ ( \sqrt{3} )^{2} - ( \sqrt{5} )^{2} } = \frac{ \sqrt{15}+5- \sqrt{3}- \sqrt{5} }{3-5}$$= \frac{ \sqrt{15}- \sqrt{3}- \sqrt{5} +5 }{-2} = \frac{ \sqrt{3}+\sqrt{5} -\sqrt{15}-5 }{2}$