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

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

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

simplify

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

- 2 - 3

Decimal Notation

- 3.73205 \dots

Solution steps

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

Multiply by the conjugate

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

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

Expand

(1 + 3) (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

∣ 3 x - 8 ∣ = 1

5 x^{2} + 15 x - 20

7 x - 5 (x - 7) = 8 x - 13

4000 (1 + \frac{0.61}{365})^{365 \cdot 8}

6 - \frac{2}{3}

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