Algebra Examples

$\frac{4}{- 1 + \sqrt{14}}$

Step 1

Multiply $\frac{4}{- 1 + \sqrt{14}}$ by $\frac{- 1 - \sqrt{14}}{- 1 - \sqrt{14}}$ .

$\frac{4}{- 1 + \sqrt{14}} \cdot \frac{- 1 - \sqrt{14}}{- 1 - \sqrt{14}}$

Step 2

Multiply $\frac{4}{- 1 + \sqrt{14}}$ by $\frac{- 1 - \sqrt{14}}{- 1 - \sqrt{14}}$ .

$\frac{4 (- 1 - \sqrt{14})}{(- 1 + \sqrt{14}) (- 1 - \sqrt{14})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (- 1 - \sqrt{14})}{1 + \sqrt{14} + \sqrt{14} \cdot - 1 - {\sqrt{14}}^{2}}$

Step 4

Simplify.

$\frac{4 (- 1 - \sqrt{14})}{- 13}$

Step 5

Move the negative in front of the fraction.

$- \frac{4 (- 1 - \sqrt{14})}{13}$

Step 6

Rewrite $- 1$ as $- 1 (1)$ .

$- \frac{4 (- 1 (1) - \sqrt{14})}{13}$

Step 7

Factor $- 1$ out of $- \sqrt{14}$ .

$- \frac{4 (- 1 (1) - (\sqrt{14}))}{13}$

Step 8

Factor $- 1$ out of $- 1 (1) - (\sqrt{14})$ .

$- \frac{4 (- 1 (1 + \sqrt{14}))}{13}$

Step 9

Simplify the expression.

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Step 9.1

Move the negative in front of the fraction.

$- - \frac{4 (1 + \sqrt{14})}{13}$

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 \frac{4 (1 + \sqrt{14})}{13}$

Step 9.3

Multiply $\frac{4 (1 + \sqrt{14})}{13}$ by $1$ .

$\frac{4 (1 + \sqrt{14})}{13}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (1 + \sqrt{14})}{13}$

Decimal Form:

$1.45897150 \dots$