Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Cancel the common factors.

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Step 5.1

Factor $2$ out of $- 4$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.61803398 \dots$