Basic Math Examples

\frac{5}{\sqrt{2} - 1}

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

Step 1

Multiply

\frac{5}{\sqrt{2} - 1}

$\frac{5}{\sqrt{2} - 1}$ by

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

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

\frac{5}{\sqrt{2} - 1} \cdot \frac{\sqrt{2} + 1}{\sqrt{2} + 1}

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

Step 2

Multiply

\frac{5}{\sqrt{2} - 1}

$\frac{5}{\sqrt{2} - 1}$ by

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

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

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

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

Step 3

Expand the denominator using the FOIL method.

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

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

Step 4

Simplify.

\frac{5 (\sqrt{2} + 1)}{1}

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

Step 5

Divide

5 (\sqrt{2} + 1)

$5 (\sqrt{2} + 1)$ by

1

$1$ .

5 (\sqrt{2} + 1)

$5 (\sqrt{2} + 1)$

Step 6

Apply the distributive property.

5 \sqrt{2} + 5 \cdot 1

$5 \sqrt{2} + 5 \cdot 1$

Step 7

Multiply

5

$5$ by

1

$1$ .

5 \sqrt{2} + 5

$5 \sqrt{2} + 5$

Step 8

The result can be shown in multiple forms.

Exact Form:

5 \sqrt{2} + 5

$5 \sqrt{2} + 5$

Decimal Form:

12.07106781 \dots

$12.07106781 \dots$