Trigonometry Examples

$\frac{- 7}{2 \sqrt{5} + 1}$

Step 1

Move the negative in front of the fraction.

$- \frac{7}{2 \sqrt{5} + 1}$

Step 2

Multiply $\frac{7}{2 \sqrt{5} + 1}$ by $\frac{2 \sqrt{5} - 1}{2 \sqrt{5} - 1}$ .

$- (\frac{7}{2 \sqrt{5} + 1} \cdot \frac{2 \sqrt{5} - 1}{2 \sqrt{5} - 1})$

Step 3

Multiply $\frac{7}{2 \sqrt{5} + 1}$ by $\frac{2 \sqrt{5} - 1}{2 \sqrt{5} - 1}$ .

$- \frac{7 (2 \sqrt{5} - 1)}{(2 \sqrt{5} + 1) (2 \sqrt{5} - 1)}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{7 (2 \sqrt{5} - 1)}{4 {\sqrt{5}}^{2} - 2 \sqrt{5} + 2 \sqrt{5} - 1}$

Step 5

Simplify.

$- \frac{7 (2 \sqrt{5} - 1)}{19}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (2 \sqrt{5} - 1)}{19}$

Decimal Form:

$- 1.27920798 \dots$