Simplify -8/(-8+ square root of 10)

$\frac{- 8}{- 8 + \sqrt{10}}$

Move the negative in front of the fraction.

$- \frac{8}{- 8 + \sqrt{10}}$

Multiply $\frac{8}{- 8 + \sqrt{10}}$ by $\frac{- 8 - \sqrt{10}}{- 8 - \sqrt{10}}$ .

$- (\frac{8}{- 8 + \sqrt{10}} \cdot \frac{- 8 - \sqrt{10}}{- 8 - \sqrt{10}})$

Multiply $\frac{8}{- 8 + \sqrt{10}}$ by $\frac{- 8 - \sqrt{10}}{- 8 - \sqrt{10}}$ .

$- \frac{8 (- 8 - \sqrt{10})}{(- 8 + \sqrt{10}) (- 8 - \sqrt{10})}$

Expand the denominator using the FOIL method.

$- \frac{8 (- 8 - \sqrt{10})}{64 + 8 \sqrt{10} + \sqrt{10} \cdot - 8 - {\sqrt{10}}^{2}}$

Simplify.

$- \frac{8 (- 8 - \sqrt{10})}{54}$

Cancel the common factor of $8$ and $54$ .

Factor $2$ out of $8 (- 8 - \sqrt{10})$ .

$- \frac{2 (4 (- 8 - \sqrt{10}))}{54}$

Cancel the common factors.

Factor $2$ out of $54$ .

$- \frac{2 (4 (- 8 - \sqrt{10}))}{2 (27)}$

Cancel the common factor.

$- \frac{2 (4 (- 8 - \sqrt{10}))}{2 \cdot 27}$

Rewrite the expression.

$- \frac{4 (- 8 - \sqrt{10})}{27}$

Rewrite $- 8$ as $- 1 (8)$ .

$- \frac{4 (- 1 (8) - \sqrt{10})}{27}$

Factor $- 1$ out of $- \sqrt{10}$ .

$- \frac{4 (- 1 (8) - (\sqrt{10}))}{27}$

Factor $- 1$ out of $- 1 (8) - (\sqrt{10})$ .

$- \frac{4 (- 1 (8 + \sqrt{10}))}{27}$

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{4 (8 + \sqrt{10})}{27}$

Multiply $- 1$ by $- 1$ .

$1 \frac{4 (8 + \sqrt{10})}{27}$

Multiply $\frac{4 (8 + \sqrt{10})}{27}$ by $1$ .

$\frac{4 (8 + \sqrt{10})}{27}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (8 + \sqrt{10})}{27}$

Decimal Form:

$1.65367076 \dots$