Trigonometry Examples

$\frac{42}{\sqrt{7} - 1}$

Step 1

Multiply $\frac{42}{\sqrt{7} - 1}$ by $\frac{\sqrt{7} + 1}{\sqrt{7} + 1}$ .

$\frac{42}{\sqrt{7} - 1} \cdot \frac{\sqrt{7} + 1}{\sqrt{7} + 1}$

Step 2

Multiply $\frac{42}{\sqrt{7} - 1}$ by $\frac{\sqrt{7} + 1}{\sqrt{7} + 1}$ .

$\frac{42 (\sqrt{7} + 1)}{(\sqrt{7} - 1) (\sqrt{7} + 1)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{42 (\sqrt{7} + 1)}{{\sqrt{7}}^{2} + \sqrt{7} - \sqrt{7} - 1}$

Step 4

Simplify.

$\frac{42 (\sqrt{7} + 1)}{6}$

Step 5

Cancel the common factor of $42$ and $6$ .

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Step 5.1

Factor $6$ out of $42 (\sqrt{7} + 1)$ .

$\frac{6 (7 (\sqrt{7} + 1))}{6}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $6$ .

$\frac{6 (7 (\sqrt{7} + 1))}{6 (1)}$

Step 5.2.2

Cancel the common factor.

$\frac{6 (7 (\sqrt{7} + 1))}{6 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{7 (\sqrt{7} + 1)}{1}$

Step 5.2.4

Divide $7 (\sqrt{7} + 1)$ by $1$ .

$7 (\sqrt{7} + 1)$

Step 6

Apply the distributive property.

$7 \sqrt{7} + 7 \cdot 1$

Step 7

Multiply $7$ by $1$ .

$7 \sqrt{7} + 7$

Step 8

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{7} + 7$

Decimal Form:

$25.52025917 \dots$