What is 2/(1-sqrt(3)) ?

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

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simplify 2/(1-sqrt(3))

simplify

\frac{2}{1 - 3}

- 1 - 3

Decimal Notation

- 2.73205 \dots

Solution steps

\frac{2}{1 - 3}

Multiply by the conjugate

\frac{1 + 3}{1 + 3}

= \frac{2 ( 1 + 3 )}{( 1 - 3 ) ( 1 + 3 )}

Expand

2 (1 + 3) : 2 + 23

Expand

(1 - 3) (1 + 3) : - 2

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

Factor out common term

2 : 2 (1 + 3)

= \frac{2 ( 1 + 3 )}{- 2}

Cancel the common factor:

2

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

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (1 + 3)

- (1 + 3) = - 1 - 3

= - 1 - 3

3 x^{2} + 6

(6 a - 5 b)^{2}

+ 1 - 1

(x - 6) (x - 2)

(5 - 9 i)^{2}