Question

Como racionalizar 1+√2/√2-2?

Answer 1

                 $\frac{1+ \sqrt{2} }{ \sqrt{2}+2 } \\ \\ = \frac{(1+ \sqrt{2})( \sqrt{2} -2) }{( \sqrt{2}+2)( \sqrt{2}-2) } \\ \\ = \frac{ \sqrt{2} -2+ \sqrt{2}. \sqrt{2}-2 \sqrt{2} }{2-4} \\ \\ = \frac{- \sqrt{2}-2+2 }{-2} \\ \\ = \frac{ \sqrt{2} }{2}$