What is 5/(1-sqrt(11)) ?

The solution to 5/(1-sqrt(11)) is -(1+sqrt(11))/2

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simplify 5/(1-sqrt(11))

simplify

\frac{5}{1 - 11}

- \frac{1 + 11}{2}

Solution steps

\frac{5}{1 - 11}

Multiply by the conjugate

\frac{1 + 11}{1 + 11}

= \frac{5 ( 1 + 11 )}{( 1 - 11 ) ( 1 + 11 )}

Expand

5 (1 + 11) : 5 + 511

Expand

(1 - 11) (1 + 11) : - 10

= \frac{5 + 5 11}{- 10}

Factor out common term

5 : 5 (1 + 11)

= \frac{5 ( 1 + 11 )}{- 10}

Factor the number:

10 = 5 \cdot 2

= \frac{5 ( 1 + 11 )}{- 5 \cdot 2}

Cancel the common factor:

5

= \frac{1 + 11}{- 2}

Apply the fraction rule:

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

= - \frac{1 + 11}{2}

\frac{9}{5 + 2}

\frac{3}{7} \cdot \frac{14}{9}

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

(- 4 + 5 i) + (8 - 7 i)

\frac{x - 5}{5} + \frac{2 x - 1}{2}