Evaluate -7/(6-2 square root of 3)

$\frac{- 7}{6 - 2 \sqrt{3}}$

Step 1

Move the negative in front of the fraction.

$- \frac{7}{6 - 2 \sqrt{3}}$

Step 2

Multiply $\frac{7}{6 - 2 \sqrt{3}}$ by $\frac{6 + 2 \sqrt{3}}{6 + 2 \sqrt{3}}$ .

$- (\frac{7}{6 - 2 \sqrt{3}} \cdot \frac{6 + 2 \sqrt{3}}{6 + 2 \sqrt{3}})$

Step 3

Multiply $\frac{7}{6 - 2 \sqrt{3}}$ by $\frac{6 + 2 \sqrt{3}}{6 + 2 \sqrt{3}}$ .

$- \frac{7 (6 + 2 \sqrt{3})}{(6 - 2 \sqrt{3}) (6 + 2 \sqrt{3})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{7 (6 + 2 \sqrt{3})}{36 + 12 \sqrt{3} - 12 \sqrt{3} - 4 {\sqrt{3}}^{2}}$

Step 5

Simplify.

$- \frac{7 (6 + 2 \sqrt{3})}{24}$

Step 6

Cancel the common factor of $6 + 2 \sqrt{3}$ and $24$ .

Factor $2$ out of $7 (6 + 2 \sqrt{3})$ .

$- \frac{2 (7 (3 + \sqrt{3}))}{24}$

Cancel the common factors.

Factor $2$ out of $24$ .

$- \frac{2 (7 (3 + \sqrt{3}))}{2 (12)}$

Cancel the common factor.

$- \frac{2 (7 (3 + \sqrt{3}))}{2 \cdot 12}$

Rewrite the expression.

$- \frac{7 (3 + \sqrt{3})}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (3 + \sqrt{3})}{12}$

Decimal Form:

$- 2.76036297 \dots$