Evaluate 5/( square root of 3-1)

$\frac{5}{\sqrt{3} - 1}$

Step 1

Multiply $\frac{5}{\sqrt{3} - 1}$ by $\frac{\sqrt{3} + 1}{\sqrt{3} + 1}$ .

$\frac{5}{\sqrt{3} - 1} \cdot \frac{\sqrt{3} + 1}{\sqrt{3} + 1}$

Step 2

Multiply $\frac{5}{\sqrt{3} - 1}$ by $\frac{\sqrt{3} + 1}{\sqrt{3} + 1}$ .

$\frac{5 (\sqrt{3} + 1)}{(\sqrt{3} - 1) (\sqrt{3} + 1)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (\sqrt{3} + 1)}{{\sqrt{3}}^{2} + \sqrt{3} - \sqrt{3} - 1}$

Step 4

Simplify.

$\frac{5 (\sqrt{3} + 1)}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (\sqrt{3} + 1)}{2}$

Decimal Form:

$6.83012701 \dots$