Algebra Examples

$\frac{- 6}{- 7 - \sqrt{13}}$

Step 1

Move the negative in front of the fraction.

$- \frac{6}{- 7 - \sqrt{13}}$

Step 2

Multiply $\frac{6}{- 7 - \sqrt{13}}$ by $\frac{- 7 + \sqrt{13}}{- 7 + \sqrt{13}}$ .

$- (\frac{6}{- 7 - \sqrt{13}} \cdot \frac{- 7 + \sqrt{13}}{- 7 + \sqrt{13}})$

Step 3

Multiply $\frac{6}{- 7 - \sqrt{13}}$ by $\frac{- 7 + \sqrt{13}}{- 7 + \sqrt{13}}$ .

$- \frac{6 (- 7 + \sqrt{13})}{(- 7 - \sqrt{13}) (- 7 + \sqrt{13})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{6 (- 7 + \sqrt{13})}{49 - 7 \sqrt{13} + 7 \sqrt{13} - {\sqrt{13}}^{2}}$

Step 5

Simplify.

$- \frac{6 (- 7 + \sqrt{13})}{36}$

Step 6

Cancel the common factors.

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Step 6.1

Factor $6$ out of $36$ .

$- \frac{6 (- 7 + \sqrt{13})}{6 \cdot 6}$

Step 6.2

Cancel the common factor.

$- \frac{6 (- 7 + \sqrt{13})}{6 \cdot 6}$

Step 6.3

Rewrite the expression.

$- \frac{- 7 + \sqrt{13}}{6}$

Step 7

Rewrite $- 7$ as $- 1 (7)$ .

$- \frac{- 1 (7) + \sqrt{13}}{6}$

Step 8

Factor $- 1$ out of $\sqrt{13}$ .

$- \frac{- 1 (7) - 1 (- \sqrt{13})}{6}$

Step 9

Factor $- 1$ out of $- 1 (7) - 1 (- \sqrt{13})$ .

$- \frac{- 1 (7 - \sqrt{13})}{6}$

Step 10

Simplify the expression.

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Step 10.1

Move the negative in front of the fraction.

$- - \frac{7 - \sqrt{13}}{6}$

Step 10.2

Multiply $- 1$ by $- 1$ .

$1 \frac{7 - \sqrt{13}}{6}$

Step 10.3

Multiply $\frac{7 - \sqrt{13}}{6}$ by $1$ .

$\frac{7 - \sqrt{13}}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{7 - \sqrt{13}}{6}$

Decimal Form:

$0.56574145 \dots$