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

- 0.26794 \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

8 - 4 (2 - x) \geq - 2 x

\frac{1.5 \cdot 1 0 ^{- 7}}{1.8 \cdot 1 0 ^{- 8}}

6 x + 8 = 3 x + 4

\frac{0}{( - 4 )}

6 x < 3 x + 15

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