Algebra Examples

$\frac{2}{\sqrt{2} + 1}$

Step 1

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

$\frac{2}{\sqrt{2} + 1} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1}$

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{2 (\sqrt{2} - 1)}{1}$

Step 5

Divide $2 (\sqrt{2} - 1)$ by $1$ .

$2 (\sqrt{2} - 1)$

Step 6

Apply the distributive property.

$2 \sqrt{2} + 2 \cdot - 1$

Step 7

Multiply $2$ by $- 1$ .

$2 \sqrt{2} - 2$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2} - 2$

Decimal Form:

$0.82842712 \dots$