What is (-8)/(3+sqrt(17)) ?

The solution to (-8)/(3+sqrt(17)) is 3-sqrt(17)

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simplify (-8)/(3+sqrt(17))

simplify

\frac{- 8}{3 + 17}

3 - 17

Solution steps

\frac{- 8}{3 + 17}

Multiply by the conjugate

\frac{3 - 17}{3 - 17}

= \frac{- 8 ( 3 - 17 )}{( 3 + 17 ) ( 3 - 17 )}

Expand

- 8 (3 - 17) : - 24 + 817

Expand

(3 + 17) (3 - 17) : - 8

= \frac{- 24 + 8 17}{- 8}

Factor out common term

8 : 8 (- 3 + 17)

= \frac{8 ( - 3 + 17 )}{- 8}

Cancel the common factor:

8

= \frac{- 3 + 17}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - (- 3 + 17)

- (- 3 + 17) = 3 - 17

= 3 - 17

50 p^{3} + 50 p^{2} - 20

\frac{14}{15}

(x + 25)^{2}

x + 1 \cdot x + 1

(4^{7})^{- 2}