Divide ( square root of 2)/(3+ square root of 2)

$\frac{\sqrt{2}}{3 + \sqrt{2}}$

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

$\frac{\sqrt{2}}{3 + \sqrt{2}} \cdot \frac{3 - \sqrt{2}}{3 - \sqrt{2}}$

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

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

Expand the denominator using the FOIL method.

$\frac{\sqrt{2} (3 - \sqrt{2})}{9 - 3 \sqrt{2} + \sqrt{2} \cdot 3 - {\sqrt{2}}^{2}}$

Simplify.

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

Apply the distributive property.

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

Move $3$ to the left of $\sqrt{2}$ .

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

Multiply $\sqrt{2} (- \sqrt{2})$ .

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \cdot \sqrt{2} - ({\sqrt{2}}^{1} \sqrt{2})}{7}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{3 \cdot \sqrt{2} - ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{7}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \cdot \sqrt{2} - {\sqrt{2}}^{1 + 1}}{7}$

Add $1$ and $1$ .

$\frac{3 \cdot \sqrt{2} - {\sqrt{2}}^{2}}{7}$

Simplify each term.

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{3 \sqrt{2} - {(2^{\frac{1}{2}})}^{2}}{7}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3 \sqrt{2} - 2^{\frac{1}{2} \cdot 2}}{7}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{3 \sqrt{2} - 2^{\frac{2}{2}}}{7}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \sqrt{2} - 2^{\frac{2}{2}}}{7}$

Rewrite the expression.

$\frac{3 \sqrt{2} - 2^{1}}{7}$

Evaluate the exponent.

$\frac{3 \sqrt{2} - 1 \cdot 2}{7}$

Multiply $- 1$ by $2$ .

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

Split the fraction $\frac{3 \sqrt{2} - 2}{7}$ into two fractions.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.32037724 \dots$

Divide ( square root of 2)/(3+ square root of 2)

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