Algebra Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

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

Step 6

Simplify the expression.

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Step 6.1

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

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

Step 6.2

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

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

Step 7

Apply the distributive property.

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

Step 8

Multiply.

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Step 8.1

Multiply $3$ by $4$ .

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

Step 8.2

Multiply $- 1$ by $3$ .

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

Step 9

Apply the distributive property.

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

Step 10

Multiply.

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Step 10.1

Multiply $- 1$ by $12$ .

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

Step 10.2

Multiply $- 3$ by $- 1$ .

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

Step 11

Apply the distributive property.

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

Step 12

Multiply.

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Step 12.1

Multiply $- 1$ by $- 12$ .

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

Step 12.2

Multiply $3$ by $- 1$ .

$12 - 3 \sqrt{17}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$12 - 3 \sqrt{17}$

Decimal Form:

$- 0.36931687 \dots$