Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Simplify the expression.

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Step 5.1

Move the negative one from the denominator of $\frac{1 - \sqrt{3}}{- 1}$ .

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

Step 5.2

Rewrite $- 1 \cdot (1 - \sqrt{3})$ as $- (1 - \sqrt{3})$ .

$- (1 - \sqrt{3})$

Step 6

Apply the distributive property.

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

Step 7

Multiply $- 1$ by $1$ .

$- 1 - - \sqrt{3}$

Step 8

Multiply $- - \sqrt{3}$ .

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Step 8.1

Multiply $- 1$ by $- 1$ .

$- 1 + 1 \sqrt{3}$

Step 8.2

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

$- 1 + \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- 1 + \sqrt{3}$

Decimal Form:

$0.73205080 \dots$