Simplify -10/(-4- square root of 17)

$\frac{- 10}{- 4 - \sqrt{17}}$

Move the negative in front of the fraction.

$- \frac{10}{- 4 - \sqrt{17}}$

Multiply $\frac{10}{- 4 - \sqrt{17}}$ by $\frac{- 4 + \sqrt{17}}{- 4 + \sqrt{17}}$ .

$- (\frac{10}{- 4 - \sqrt{17}} \cdot \frac{- 4 + \sqrt{17}}{- 4 + \sqrt{17}})$

Multiply $\frac{10}{- 4 - \sqrt{17}}$ by $\frac{- 4 + \sqrt{17}}{- 4 + \sqrt{17}}$ .

$- \frac{10 (- 4 + \sqrt{17})}{(- 4 - \sqrt{17}) (- 4 + \sqrt{17})}$

Expand the denominator using the FOIL method.

$- \frac{10 (- 4 + \sqrt{17})}{16 - 4 \sqrt{17} + 4 \sqrt{17} - {\sqrt{17}}^{2}}$

Simplify.

$- \frac{10 (- 4 + \sqrt{17})}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{10 (- 4 + \sqrt{17})}{- 1}$ .

$- (- 1 \cdot (10 (- 4 + \sqrt{17})))$

Rewrite $- 1 \cdot (10 (- 4 + \sqrt{17}))$ as $- (10 (- 4 + \sqrt{17}))$ .

$- - (10 (- 4 + \sqrt{17}))$

Apply the distributive property.

$- - (10 \cdot - 4 + 10 \sqrt{17})$

Multiply $10$ by $- 4$ .

$- - (- 40 + 10 \sqrt{17})$

Apply the distributive property.

$- (- - 40 - (10 \sqrt{17}))$

Multiply.

Multiply $- 1$ by $- 40$ .

$- (40 - (10 \sqrt{17}))$

Multiply $10$ by $- 1$ .

$- (40 - 10 \sqrt{17})$

Apply the distributive property.

$- 1 \cdot 40 - (- 10 \sqrt{17})$

Multiply.

Multiply $- 1$ by $40$ .

$- 40 - (- 10 \sqrt{17})$

Multiply $- 10$ by $- 1$ .

$- 40 + 10 \sqrt{17}$

The result can be shown in multiple forms.

Exact Form:

$- 40 + 10 \sqrt{17}$

Decimal Form:

$1.23105625 \dots$