Question

Calcule o valor de:
$\frac{1}{1 - \sqrt{2} } - \frac{1}{1 + \sqrt{2} } + 1$
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Answer 1

Resposta:

$2(1-\sqrt{2})$

Explicação passo a passo:

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