What is 5/(1+sqrt(3)) ?

The solution to 5/(1+sqrt(3)) is -(5-5sqrt(3))/2

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simplify 5/(1+sqrt(3))

simplify

\frac{5}{1 + 3}

- \frac{5 - 5 3}{2}

Solution steps

\frac{5}{1 + 3}

Multiply by the conjugate

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

= \frac{5 ( 1 - 3 )}{( 1 + 3 ) ( 1 - 3 )}

Expand

5 (1 - 3) : 5 - 53

Expand

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

= \frac{5 - 5 3}{- 2}

Apply the fraction rule:

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

= - \frac{5 - 5 3}{2}

5 x - 9 = 4 (x - 12)

\frac{5}{6} (- 3)

(x^{3})^{\frac{3}{2}}

2 7^{- \frac{1}{2}}

\frac{2 ^{0.01} - 1}{0.01}