Trigonometry Examples

$\frac{6}{4 - \sqrt{2}}$

Step 1

Multiply $\frac{6}{4 - \sqrt{2}}$ by $\frac{4 + \sqrt{2}}{4 + \sqrt{2}}$ .

$\frac{6}{4 - \sqrt{2}} \cdot \frac{4 + \sqrt{2}}{4 + \sqrt{2}}$

Step 2

Multiply $\frac{6}{4 - \sqrt{2}}$ by $\frac{4 + \sqrt{2}}{4 + \sqrt{2}}$ .

$\frac{6 (4 + \sqrt{2})}{(4 - \sqrt{2}) (4 + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (4 + \sqrt{2})}{16 + 4 \sqrt{2} - 4 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{6 (4 + \sqrt{2})}{14}$

Step 5

Cancel the common factor of $6$ and $14$ .

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Step 5.1

Factor $2$ out of $6 (4 + \sqrt{2})$ .

$\frac{2 (3 (4 + \sqrt{2}))}{14}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $14$ .

$\frac{2 (3 (4 + \sqrt{2}))}{2 (7)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (3 (4 + \sqrt{2}))}{2 \cdot 7}$

Step 5.2.3

Rewrite the expression.

$\frac{3 (4 + \sqrt{2})}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (4 + \sqrt{2})}{7}$

Decimal Form:

$2.32037724 \dots$