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

The solution to (1-sqrt(2))/(1+sqrt(2)) is -3+2sqrt(2)

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simplify (1-sqrt(2))/(1+sqrt(2))

simplify

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

- 3 + 22

Decimal Notation

- 0.17157 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(1 - 2) (1 - 2) : 3 - 22

Expand

(1 + 2) (1 - 2) : - 1

= \frac{3 - 2 2}{- 1}

\frac{3 - 2 2}{- 1} = - 3 + 22

= - 3 + 22

\frac{( x - 3 ) ( x + 2 )}{x ^{2} - 9} \cdot \frac{5}{x + 2}

\frac{9 x ^{5} + 9 x ^{4} + 45 x ^{3}}{9 x ^{2}}

3 \frac{8}{9}

\frac{5 r ^{- 1}}{4 ( r ^{- 1} ) ^{2}}

x^{4} - 5 x^{3} + 5 x^{2} + 5 x - 6

What is (1-sqrt(2))/(1+sqrt(2)) ?
The solution to (1-sqrt(2))/(1+sqrt(2)) is -3+2sqrt(2)