Simplify -1/(2+ square root of 3)

$- \frac{1}{2 + \sqrt{3}}$

Step 1

Multiply $\frac{1}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

$- (\frac{1}{2 + \sqrt{3}} \cdot \frac{2 - \sqrt{3}}{2 - \sqrt{3}})$

Step 2

Multiply $\frac{1}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$- \frac{2 - \sqrt{3}}{4 - 2 \sqrt{3} + \sqrt{3} \cdot 2 - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$- \frac{2 - \sqrt{3}}{1}$

Step 5

Divide $2 - \sqrt{3}$ by $1$ .

$- (2 - \sqrt{3})$

Step 6

Apply the distributive property.

$- 1 \cdot 2 - - \sqrt{3}$

Step 7

Multiply $- 1$ by $2$ .

$- 2 - - \sqrt{3}$

Step 8

Multiply $- - \sqrt{3}$ .

Multiply $- 1$ by $- 1$ .

$- 2 + 1 \sqrt{3}$

Multiply $\sqrt{3}$ by $1$ .

$- 2 + \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- 2 + \sqrt{3}$

Decimal Form:

$- 0.26794919 \dots$