What is 1/(1+sqrt(2)) ?

The solution to 1/(1+sqrt(2)) is sqrt(2)-1

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simplify 1/(1+sqrt(2))

simplify

\frac{1}{1 + 2}

2 - 1

Solution steps

\frac{1}{1 + 2}

Multiply by the conjugate

\frac{1 - 2}{1 - 2}

= \frac{1 \cdot ( 1 - 2 )}{( 1 + 2 ) ( 1 - 2 )}

1 \cdot (1 - 2) = 1 - 2

(1 + 2) (1 - 2) = - 1

= \frac{1 - 2}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

1 - 2 = - (2 - 1)

= \frac{2 - 1}{1}

Apply rule

\frac{a}{1} = a

= 2 - 1

(k + 8) (k - 8)

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x - 2^{2}

- 4 + (- 5)