Simplify -3/(4+ square root of 17)

$\frac{- 3}{4 + \sqrt{17}}$

Move the negative in front of the fraction.

$- \frac{3}{4 + \sqrt{17}}$

Multiply $\frac{3}{4 + \sqrt{17}}$ by $\frac{4 - \sqrt{17}}{4 - \sqrt{17}}$ .

$- (\frac{3}{4 + \sqrt{17}} \cdot \frac{4 - \sqrt{17}}{4 - \sqrt{17}})$

Multiply $\frac{3}{4 + \sqrt{17}}$ by $\frac{4 - \sqrt{17}}{4 - \sqrt{17}}$ .

$- \frac{3 (4 - \sqrt{17})}{(4 + \sqrt{17}) (4 - \sqrt{17})}$

Expand the denominator using the FOIL method.

$- \frac{3 (4 - \sqrt{17})}{16 - 4 \sqrt{17} + \sqrt{17} \cdot 4 - {\sqrt{17}}^{2}}$

Simplify.

$- \frac{3 (4 - \sqrt{17})}{- 1}$

Simplify the expression.

Move the negative one from the denominator of $\frac{3 (4 - \sqrt{17})}{- 1}$ .

$- (- 1 \cdot (3 (4 - \sqrt{17})))$

Rewrite $- 1 \cdot (3 (4 - \sqrt{17}))$ as $- (3 (4 - \sqrt{17}))$ .

$- - (3 (4 - \sqrt{17}))$

Apply the distributive property.

$- - (3 \cdot 4 + 3 (- \sqrt{17}))$

Multiply.

Multiply $3$ by $4$ .

$- - (12 + 3 (- \sqrt{17}))$

Multiply $- 1$ by $3$ .

$- - (12 - 3 \sqrt{17})$

Apply the distributive property.

$- (- 1 \cdot 12 - (- 3 \sqrt{17}))$

Multiply.

Multiply $- 1$ by $12$ .

$- (- 12 - (- 3 \sqrt{17}))$

Multiply $- 3$ by $- 1$ .

$- (- 12 + 3 \sqrt{17})$

Apply the distributive property.

$- - 12 - (3 \sqrt{17})$

Multiply.

Multiply $- 1$ by $- 12$ .

$12 - (3 \sqrt{17})$

Multiply $3$ by $- 1$ .

$12 - 3 \sqrt{17}$

The result can be shown in multiple forms.

Exact Form:

$12 - 3 \sqrt{17}$

Decimal Form:

$- 0.36931687 \dots$