Algebra Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

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

Step 6

Cancel the common factors.

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Step 6.1

Factor $4$ out of $- 16$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

Move the negative in front of the fraction.

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

Step 8

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

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Step 8.1

Multiply $- 1$ by $- 1$ .

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

Step 8.2

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

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

Step 9

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

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

Step 10

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

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

Step 11

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

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

Step 12

Move the negative in front of the fraction.

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

Step 13

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.78077640 \dots$