Basic Math Examples

$\frac{- 6}{5 - \sqrt{11}}$

Step 1

Move the negative in front of the fraction.

$- \frac{6}{5 - \sqrt{11}}$

Step 2

Multiply

$\frac{6}{5 - \sqrt{11}}$ by

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

$- (\frac{6}{5 - \sqrt{11}} \cdot \frac{5 + \sqrt{11}}{5 + \sqrt{11}})$

Step 3

Multiply

$\frac{6}{5 - \sqrt{11}}$ by

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

$- \frac{6 (5 + \sqrt{11})}{(5 - \sqrt{11}) (5 + \sqrt{11})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{6 (5 + \sqrt{11})}{25 + 5 \sqrt{11} - 5 \sqrt{11} - {\sqrt{11}}^{2}}$

Step 5

Simplify.

$- \frac{6 (5 + \sqrt{11})}{14}$

Step 6

Cancel the common factor of

$6$ and

$14$ .

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Step 6.1

Factor

$2$ out of

$6 (5 + \sqrt{11})$ .

$- \frac{2 (3 (5 + \sqrt{11}))}{14}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

$2$ out of

$14$ .

$- \frac{2 (3 (5 + \sqrt{11}))}{2 (7)}$

Step 6.2.2

Cancel the common factor.

$- \frac{2 (3 (5 + \sqrt{11}))}{2 \cdot 7}$

Step 6.2.3

Rewrite the expression.

$- \frac{3 (5 + \sqrt{11})}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 (5 + \sqrt{11})}{7}$

Decimal Form:

$- 3.56426776 \dots$