Rationalize the Denominator -4/(-1- square root of 17)

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Algebra

$\frac{- 4}{- 1 - \sqrt{17}}$

Move the negative in front of the fraction.

$- \frac{4}{- 1 - \sqrt{17}}$

Multiply $\frac{4}{- 1 - \sqrt{17}}$ by $\frac{- 1 + \sqrt{17}}{- 1 + \sqrt{17}}$ .

$- (\frac{4}{- 1 - \sqrt{17}} \cdot \frac{- 1 + \sqrt{17}}{- 1 + \sqrt{17}})$

Multiply $\frac{4}{- 1 - \sqrt{17}}$ and $\frac{- 1 + \sqrt{17}}{- 1 + \sqrt{17}}$ .

$- \frac{4 (- 1 + \sqrt{17})}{(- 1 - \sqrt{17}) (- 1 + \sqrt{17})}$

Expand the denominator using the FOIL method.

$- \frac{4 (- 1 + \sqrt{17})}{1 - \sqrt{17} + \sqrt{17} - {\sqrt{17}}^{2}}$

Simplify.

$- \frac{4 (- 1 + \sqrt{17})}{- 16}$

Cancel the common factors.

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Factor $4$ out of $- 16$ .

$- \frac{4 (- 1 + \sqrt{17})}{4 \cdot - 4}$

Cancel the common factor.

$- \frac{4 (- 1 + \sqrt{17})}{4 \cdot - 4}$

Rewrite the expression.

$- \frac{- 1 + \sqrt{17}}{- 4}$

Move the negative in front of the fraction.

$- - \frac{- 1 + \sqrt{17}}{4}$

Multiply $- - \frac{- 1 + \sqrt{17}}{4}$ .

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Multiply $- 1$ by $- 1$ .

$1 \frac{- 1 + \sqrt{17}}{4}$

Multiply $\frac{- 1 + \sqrt{17}}{4}$ by $1$ .

$\frac{- 1 + \sqrt{17}}{4}$

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 (1) + \sqrt{17}}{4}$

Factor $- 1$ out of $\sqrt{17}$ .

$\frac{- 1 (1) - 1 (- \sqrt{17})}{4}$

Factor $- 1$ out of $- 1 (1) - 1 (- \sqrt{17})$ .

$\frac{- 1 (1 - \sqrt{17})}{4}$

Move the negative in front of the fraction.

$- \frac{1 - \sqrt{17}}{4}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1 - \sqrt{17}}{4}$

Decimal Form:

$0.78077640 \dots$

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