Question

Спростіть вираз:(√2+1/√2 - 1/√2-1)× √2/2

Answer 1

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