Divide 3/( square root of 3-1)

$\frac{3}{\sqrt{3} - 1}$

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

Apply the distributive property.

$\frac{3 \sqrt{3} + 3 \cdot 1}{2}$

Multiply $3$ by $1$ .

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$4.09807621 \dots$