Basic Math Examples

\frac{2}{5 - \sqrt{3}}

$\frac{2}{5 - \sqrt{3}}$

Step 1

Multiply

\frac{2}{5 - \sqrt{3}}

$\frac{2}{5 - \sqrt{3}}$ by

\frac{5 + \sqrt{3}}{5 + \sqrt{3}}

$\frac{5 + \sqrt{3}}{5 + \sqrt{3}}$ .

\frac{2}{5 - \sqrt{3}} \cdot \frac{5 + \sqrt{3}}{5 + \sqrt{3}}

$\frac{2}{5 - \sqrt{3}} \cdot \frac{5 + \sqrt{3}}{5 + \sqrt{3}}$

Step 2

Multiply

\frac{2}{5 - \sqrt{3}}

$\frac{2}{5 - \sqrt{3}}$ by

\frac{5 + \sqrt{3}}{5 + \sqrt{3}}

$\frac{5 + \sqrt{3}}{5 + \sqrt{3}}$ .

\frac{2 (5 + \sqrt{3})}{(5 - \sqrt{3}) (5 + \sqrt{3})}

$\frac{2 (5 + \sqrt{3})}{(5 - \sqrt{3}) (5 + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

\frac{2 (5 + \sqrt{3})}{25 + 5 \sqrt{3} - 5 \sqrt{3} - {\sqrt{3}}^{2}}

$\frac{2 (5 + \sqrt{3})}{25 + 5 \sqrt{3} - 5 \sqrt{3} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

\frac{2 (5 + \sqrt{3})}{22}

$\frac{2 (5 + \sqrt{3})}{22}$

Step 5

Cancel the common factors.

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Step 5.1

Factor

2

$2$ out of

22

$22$ .

\frac{2 (5 + \sqrt{3})}{2 \cdot 11}

$\frac{2 (5 + \sqrt{3})}{2 \cdot 11}$

Step 5.2

Cancel the common factor.

$\frac{2 (5 + \sqrt{3})}{2 \cdot 11}$

Step 5.3

Rewrite the expression.

$\frac{5 + \sqrt{3}}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 + \sqrt{3}}{11}$

Decimal Form:

$0.61200461 \dots$