Algebra Examples

$\frac{- 2}{- 4 + \sqrt{14}}$

Step 1

Move the negative in front of the fraction.

$- \frac{2}{- 4 + \sqrt{14}}$

Step 2

Multiply $\frac{2}{- 4 + \sqrt{14}}$ by $\frac{- 4 - \sqrt{14}}{- 4 - \sqrt{14}}$ .

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

Step 3

Multiply $\frac{2}{- 4 + \sqrt{14}}$ by $\frac{- 4 - \sqrt{14}}{- 4 - \sqrt{14}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{2 (- 4 - \sqrt{14})}{16 + 4 \sqrt{14} + \sqrt{14} \cdot - 4 - {\sqrt{14}}^{2}}$

Step 5

Simplify.

$- \frac{2 (- 4 - \sqrt{14})}{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

$- \frac{2 (- 4 - \sqrt{14})}{2}$

Step 6.2

Divide $- 4 - \sqrt{14}$ by $1$ .

$- (- 4 - \sqrt{14})$

Step 7

Apply the distributive property.

$- - 4 - - \sqrt{14}$

Step 8

Multiply $- 1$ by $- 4$ .

$4 - - \sqrt{14}$

Step 9

Multiply $- - \sqrt{14}$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$4 + 1 \sqrt{14}$

Step 9.2

Multiply $\sqrt{14}$ by $1$ .

$4 + \sqrt{14}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$4 + \sqrt{14}$

Decimal Form:

$7.74165738 \dots$