Simplify -2/(-4+ square root of 14)

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

Move the negative in front of the fraction.

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Apply the distributive property.

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

Multiply $- 1$ by $- 4$ .

$4 - - \sqrt{14}$

Multiply $- - \sqrt{14}$ .

Multiply $- 1$ by $- 1$ .

$4 + 1 \sqrt{14}$

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

$4 + \sqrt{14}$

The result can be shown in multiple forms.

Exact Form:

$4 + \sqrt{14}$

Decimal Form:

$7.74165738 \dots$