Simplify 4/(4- square root of 6x)

$\frac{4}{4 - \sqrt{6 x}}$

Multiply $\frac{4}{4 - \sqrt{6 x}}$ by $\frac{4 + \sqrt{6 x}}{4 + \sqrt{6 x}}$ .

$\frac{4}{4 - \sqrt{6 x}} \cdot \frac{4 + \sqrt{6 x}}{4 + \sqrt{6 x}}$

Multiply $\frac{4}{4 - \sqrt{6 x}}$ by $\frac{4 + \sqrt{6 x}}{4 + \sqrt{6 x}}$ .

$\frac{4 (4 + \sqrt{6 x})}{(4 - \sqrt{6 x}) (4 + \sqrt{6 x})}$

Expand the denominator using the FOIL method.

$\frac{4 (4 + \sqrt{6 x})}{16 + 4 \sqrt{6 x} - 4 \sqrt{6 x} - {\sqrt{6 x}}^{2}}$

Simplify.

Rewrite ${\sqrt{6 x}}^{2}$ as $6 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x}$ as ${(6 x)}^{\frac{1}{2}}$ .

$\frac{4 (4 + \sqrt{6 x})}{16 - {({(6 x)}^{\frac{1}{2}})}^{2}}$

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

$\frac{4 (4 + \sqrt{6 x})}{16 - {(6 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{4 (4 + \sqrt{6 x})}{16 - {(6 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 (4 + \sqrt{6 x})}{16 - {(6 x)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{4 (4 + \sqrt{6 x})}{16 - {(6 x)}^{1}}$

Simplify.

$\frac{4 (4 + \sqrt{6 x})}{16 - (6 x)}$

Multiply $6$ by $- 1$ .

$\frac{4 (4 + \sqrt{6 x})}{16 - 6 x}$

Cancel the common factor of $4$ and $16 - 6 x$ .

Factor $2$ out of $4 (4 + \sqrt{6 x})$ .

$\frac{2 (2 (4 + \sqrt{6 x}))}{16 - 6 x}$

Cancel the common factors.

Factor $2$ out of $16$ .

$\frac{2 (2 (4 + \sqrt{6 x}))}{2 (8) - 6 x}$

Factor $2$ out of $- 6 x$ .

$\frac{2 (2 (4 + \sqrt{6 x}))}{2 (8) + 2 (- 3 x)}$

Factor $2$ out of $2 (8) + 2 (- 3 x)$ .

$\frac{2 (2 (4 + \sqrt{6 x}))}{2 (8 - 3 x)}$

Cancel the common factor.

$\frac{2 (2 (4 + \sqrt{6 x}))}{2 (8 - 3 x)}$

Rewrite the expression.

$\frac{2 (4 + \sqrt{6 x})}{8 - 3 x}$