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

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

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simplify 2/(2-sqrt(2))

simplify

\frac{2}{2 - 2}

2 + 2

Decimal Notation

3.41421 \dots

Solution steps

\frac{2}{2 - 2}

Multiply by the conjugate

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

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

Expand

2 (2 + 2) : 4 + 22

Expand

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

= \frac{4 + 2 2}{2}

Factor out common term

2 : 2 (2 + 2)

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

Cancel the common factor:

2

= 2 + 2

x \cdot (- 3) x

- 30 x^{4} y + 24 x z^{3}

(u + 4)^{2}

\frac{8}{6 - 2}

1 + 729 x^{6}