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

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

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simplify (sqrt(3)+1)/(1-sqrt(3))

simplify

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

- 2 - 3

Decimal Notation

- 3.73205 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(3 + 1) (1 + 3) : 4 + 23

Expand

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

= \frac{4 + 2 3}{- 2}

Factor out common term

2 : 2 (2 + 3)

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

Cancel the common factor:

2

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

Apply the fraction rule:

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

= - (2 + 3)

- (2 + 3) = - 2 - 3

= - 2 - 3

1 - \frac{2}{9}

10 b - 90

(2^{5})^{- 3}

a y - 4 b y + 4 a x - 16 b x

b^{2} - 36

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