Simplify -6/(-7- square root of 11)

$\frac{- 6}{- 7 - \sqrt{11}}$

Step 1

Move the negative in front of the fraction.

$- \frac{6}{- 7 - \sqrt{11}}$

Step 2

Multiply $\frac{6}{- 7 - \sqrt{11}}$ by $\frac{- 7 + \sqrt{11}}{- 7 + \sqrt{11}}$ .

$- (\frac{6}{- 7 - \sqrt{11}} \cdot \frac{- 7 + \sqrt{11}}{- 7 + \sqrt{11}})$

Step 3

Multiply $\frac{6}{- 7 - \sqrt{11}}$ by $\frac{- 7 + \sqrt{11}}{- 7 + \sqrt{11}}$ .

$- \frac{6 (- 7 + \sqrt{11})}{(- 7 - \sqrt{11}) (- 7 + \sqrt{11})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{6 (- 7 + \sqrt{11})}{49 - 7 \sqrt{11} + 7 \sqrt{11} - {\sqrt{11}}^{2}}$

Step 5

Simplify.

$- \frac{6 (- 7 + \sqrt{11})}{38}$

Step 6

Cancel the common factor of $6$ and $38$ .

Factor $2$ out of $6 (- 7 + \sqrt{11})$ .

$- \frac{2 (3 (- 7 + \sqrt{11}))}{38}$

Cancel the common factors.

Factor $2$ out of $38$ .

$- \frac{2 (3 (- 7 + \sqrt{11}))}{2 (19)}$

Cancel the common factor.

$- \frac{2 (3 (- 7 + \sqrt{11}))}{2 \cdot 19}$

Rewrite the expression.

$- \frac{3 (- 7 + \sqrt{11})}{19}$

Step 7

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

$- \frac{3 (- 1 (7) + \sqrt{11})}{19}$

Step 8

Factor $- 1$ out of $\sqrt{11}$ .

$- \frac{3 (- 1 (7) - 1 (- \sqrt{11}))}{19}$

Step 9

Factor $- 1$ out of $- 1 (7) - 1 (- \sqrt{11})$ .

$- \frac{3 (- 1 (7 - \sqrt{11}))}{19}$

Step 10

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{3 (7 - \sqrt{11})}{19}$

Multiply $- 1$ by $- 1$ .

$1 \frac{3 (7 - \sqrt{11})}{19}$

Multiply $\frac{3 (7 - \sqrt{11})}{19}$ by $1$ .

$\frac{3 (7 - \sqrt{11})}{19}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (7 - \sqrt{11})}{19}$

Decimal Form:

$0.58158555 \dots$

Simplify -6/(-7- square root of 11)

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