Trigonometry Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Multiply $\frac{5}{6 + \sqrt{11}}$ by $\frac{6 - \sqrt{11}}{6 - \sqrt{11}}$ .

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

Step 3

Multiply $\frac{5}{6 + \sqrt{11}}$ by $\frac{6 - \sqrt{11}}{6 - \sqrt{11}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{5 (6 - \sqrt{11})}{36 - 6 \sqrt{11} + \sqrt{11} \cdot 6 - {\sqrt{11}}^{2}}$

Step 5

Simplify.

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

Step 6

Cancel the common factors.

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Step 6.1

Factor $5$ out of $25$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.53667504 \dots$