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

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

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simplify (sqrt(2))/(2-sqrt(2))

simplify

\frac{2}{2 - 2}

2 + 1

Decimal Notation

2.41421 \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) : 22 + 2

Expand

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

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

Factor out common term

2 : 2 (2 + 1)

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

Cancel the common factor:

2

= 2 + 1

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lo g_{10} (1 0^{5}) + 3 lo g_{10} (1 0^{7})

\frac{2}{6} \div \frac{3}{10}

\frac{7}{3 x ^{2} - 75} + \frac{3}{2 x + 10}

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