Basic Math Examples

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

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.2

Cancel the common factor.

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

Step 1.3

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

$- 1 \cdot \frac{2 + \sqrt{3}}{4 + 2 \sqrt{3} - 2 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 5

Simplify.

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

Step 6

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

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

Step 7

Apply the distributive property.

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

Step 8

Simplify the expression.

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Step 8.1

Multiply $- 1$ by $2$ .

$- 2 - 1 \sqrt{3}$

Step 8.2

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$- 2 - \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- 2 - \sqrt{3}$

Decimal Form:

$- 3.73205080 \dots$