Simplify 5/(-4- square root of 6)

$\frac{5}{- 4 - \sqrt{6}}$

Multiply $\frac{5}{- 4 - \sqrt{6}}$ by $\frac{- 4 + \sqrt{6}}{- 4 + \sqrt{6}}$ .

$\frac{5}{- 4 - \sqrt{6}} \cdot \frac{- 4 + \sqrt{6}}{- 4 + \sqrt{6}}$

Multiply $\frac{5}{- 4 - \sqrt{6}}$ by $\frac{- 4 + \sqrt{6}}{- 4 + \sqrt{6}}$ .

$\frac{5 (- 4 + \sqrt{6})}{(- 4 - \sqrt{6}) (- 4 + \sqrt{6})}$

Expand the denominator using the FOIL method.

$\frac{5 (- 4 + \sqrt{6})}{16 - 4 \sqrt{6} + 4 \sqrt{6} - {\sqrt{6}}^{2}}$

Simplify.

$\frac{5 (- 4 + \sqrt{6})}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (- 4 + \sqrt{6})}{5 \cdot 2}$

Cancel the common factor.

$\frac{5 (- 4 + \sqrt{6})}{5 \cdot 2}$

Rewrite the expression.

$\frac{- 4 + \sqrt{6}}{2}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + \sqrt{6}}{2}$

Factor $- 1$ out of $\sqrt{6}$ .

$\frac{- 1 (4) - 1 (- \sqrt{6})}{2}$

Factor $- 1$ out of $- 1 (4) - 1 (- \sqrt{6})$ .

$\frac{- 1 (4 - \sqrt{6})}{2}$

Move the negative in front of the fraction.

$- \frac{4 - \sqrt{6}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 - \sqrt{6}}{2}$

Decimal Form:

$- 0.77525512 \dots$