Evaluate 2/( square root of 5-1)

$\frac{2}{\sqrt{5} - 1}$

Step 1

Multiply $\frac{2}{\sqrt{5} - 1}$ by $\frac{\sqrt{5} + 1}{\sqrt{5} + 1}$ .

$\frac{2}{\sqrt{5} - 1} \cdot \frac{\sqrt{5} + 1}{\sqrt{5} + 1}$

Step 2

Multiply $\frac{2}{\sqrt{5} - 1}$ by $\frac{\sqrt{5} + 1}{\sqrt{5} + 1}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{2 (\sqrt{5} + 1)}{4}$

Step 5

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{\sqrt{5} + 1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5} + 1}{2}$

Decimal Form:

$1.61803398 \dots$