Simplify 1/(4 square root of 6+ square root of 3)

$\frac{1}{4 \sqrt{6} + \sqrt{3}}$

Multiply $\frac{1}{4 \sqrt{6} + \sqrt{3}}$ by $\frac{4 \sqrt{6} - \sqrt{3}}{4 \sqrt{6} - \sqrt{3}}$ .

$\frac{1}{4 \sqrt{6} + \sqrt{3}} \cdot \frac{4 \sqrt{6} - \sqrt{3}}{4 \sqrt{6} - \sqrt{3}}$

Multiply $\frac{1}{4 \sqrt{6} + \sqrt{3}}$ by $\frac{4 \sqrt{6} - \sqrt{3}}{4 \sqrt{6} - \sqrt{3}}$ .

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

Expand the denominator using the FOIL method.

$\frac{4 \sqrt{6} - \sqrt{3}}{16 {\sqrt{6}}^{2} - 4 \sqrt{18} + 4 \sqrt{18} - {\sqrt{3}}^{2}}$

Simplify.

$\frac{4 \sqrt{6} - \sqrt{3}}{93}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{6} - \sqrt{3}}{93}$

Decimal Form:

$0.08673019 \dots$