Simplify 3/( square root of 2- square root of y)

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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