What is 8/(1-sqrt(17)) ?

The solution to 8/(1-sqrt(17)) is -(1+sqrt(17))/2

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simplify 8/(1-sqrt(17))

simplify

\frac{8}{1 - 17}

- \frac{1 + 17}{2}

Decimal Notation

- 2.56155 \dots

Solution steps

\frac{8}{1 - 17}

Multiply by the conjugate

\frac{1 + 17}{1 + 17}

= \frac{8 ( 1 + 17 )}{( 1 - 17 ) ( 1 + 17 )}

Expand

8 (1 + 17) : 8 + 817

Expand

(1 - 17) (1 + 17) : - 16

= \frac{8 + 8 17}{- 16}

Factor out common term

8 : 8 (1 + 17)

= \frac{8 ( 1 + 17 )}{- 16}

Factor the number:

16 = 8 \cdot 2

= \frac{8 ( 1 + 17 )}{- 8 \cdot 2}

Cancel the common factor:

8

= \frac{1 + 17}{- 2}

Apply the fraction rule:

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

= - \frac{1 + 17}{2}

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