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}

Decimal Notation

- 4.09807 \dots

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}

\frac{144}{( - 12 )}

- x^{3} + 2 x^{2}

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

x^{4} x^{2}

y^{2} \cdot y