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

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

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simplify 2/(sqrt(2)-1)

simplify

\frac{2}{2 - 1}

22 + 2

Decimal Notation

4.82842 \dots

Solution steps

\frac{2}{2 - 1}

Multiply by the conjugate

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

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

Expand

2 (2 + 1) : 22 + 2

Expand

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

= \frac{2 2 + 2}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 22 + 2

\frac{5}{1} + \frac{1}{2}

i^{624}

\frac{4}{2 + 7}

\frac{( - 1 ) ^{2 - 1}}{2 ^{2}}

3^{2 l o g_{3} (7)}