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

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

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simplify 1/(1+sqrt(3))

simplify

\frac{1}{1 + 3}

\frac{3 - 1}{2}

Solution steps

\frac{1}{1 + 3}

Multiply by the conjugate

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

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

1 \cdot (1 - 3) = 1 - 3

(1 + 3) (1 - 3) = - 2

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

Apply the fraction rule:

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

1 - 3 = - (3 - 1)

= \frac{3 - 1}{2}

2 x^{2} + 2 x - 24

\frac{\frac{2}{b} + \frac{2}{a}}{\frac{2}{ab}}

\frac{4}{9} (- \frac{9}{4})

0.75 \cdot 2

x + 13 = 4 x + 4