Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Multiply $\frac{3}{7 + 2 \sqrt{5}}$ by $\frac{7 - 2 \sqrt{5}}{7 - 2 \sqrt{5}}$ .

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

Step 3

Multiply $\frac{3}{7 + 2 \sqrt{5}}$ by $\frac{7 - 2 \sqrt{5}}{7 - 2 \sqrt{5}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{3 (7 - 2 \sqrt{5})}{49 - 14 \sqrt{5} + 14 \sqrt{5} - 4 {\sqrt{5}}^{2}}$

Step 5

Simplify.

$- \frac{3 (7 - 2 \sqrt{5})}{29}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 (7 - 2 \sqrt{5})}{29}$

Decimal Form:

$- 0.26150317 \dots$