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

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

Move the negative in front of the fraction.

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

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.

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

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.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.77525512 \dots$