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

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

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simplify 3/(1+sqrt(3))

simplify

\frac{3}{1 + 3}

- \frac{3 - 3 3}{2}

Solution steps

\frac{3}{1 + 3}

Multiply by the conjugate

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

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

Expand

3 (1 - 3) : 3 - 33

Expand

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

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

Apply the fraction rule:

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

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

(a + 2) (a^{2} - 2 a + 4)

9 \cdot (- 9)

(x + x^{- 1})^{3}

\frac{13}{49}

- y^{2} + 6 y^{2} + 3 y^{2} + 5 y + 4 y + 3 - 1