What is 5/(-5-3sqrt(3)) ?

The solution to 5/(-5-3sqrt(3)) is -(-25+15sqrt(3))/2

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simplify 5/(-5-3sqrt(3))

simplify

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

- \frac{- 25 + 15 3}{2}

Decimal Notation

- 0.49038 \dots

Solution steps

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

Multiply by the conjugate

\frac{- 5 + 3 3}{- 5 + 3 3}

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

Expand

5 (- 5 + 33) : - 25 + 153

Expand

(- 5 - 33) (- 5 + 33) : - 2

= \frac{- 25 + 15 3}{- 2}

Apply the fraction rule:

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

= - \frac{- 25 + 15 3}{2}

- 17 + \frac{n}{5} = 33

x^{3} - 30 x

2 x + 5 \geq 19

1 - \frac{2 u - 3}{4} = \frac{2 - 5 u}{3} - 3 u

(5)^{5}