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

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

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simplify 1/(1-sqrt(2))

simplify

\frac{1}{1 - 2}

- 1 - 2

Decimal Notation

- 2.41421 \dots

Solution steps

\frac{1}{1 - 2}

Multiply by the conjugate

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

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

1 \cdot (1 + 2) = 1 + 2

(1 - 2) (1 + 2) = - 1

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

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

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

Apply rule

\frac{a}{1} = a

= - (1 + 2)

Distribute parentheses

= - (1) - (2)

Apply minus-plus rules

+ (- a) = - a

= - 1 - 2

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

(3 m - 2 n)^{2}

(x - 18)^{2}

lo g_{2} (lo g_{5} (625))

21. 3^{2} - 21. 2^{2}