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

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

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

simplify

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

3 - 22

Decimal Notation

0.17157 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

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

Expand

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

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

Apply the fraction rule:

\frac{a}{1} = a

= 3 - 22

\frac{31}{6}

\frac{5 a}{3 a}

\frac{8 x ^{4} y ^{4}}{4 x ^{8} y ^{5}}

\frac{2}{x + 2} - \frac{4}{( x + 2 ) ^{2}}

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