Algebra Examples

$\frac{- 4}{3 + \sqrt{13}}$

Step 1

Move the negative in front of the fraction.

$- \frac{4}{3 + \sqrt{13}}$

Step 2

Multiply $\frac{4}{3 + \sqrt{13}}$ by $\frac{3 - \sqrt{13}}{3 - \sqrt{13}}$ .

$- (\frac{4}{3 + \sqrt{13}} \cdot \frac{3 - \sqrt{13}}{3 - \sqrt{13}})$

Step 3

Multiply $\frac{4}{3 + \sqrt{13}}$ by $\frac{3 - \sqrt{13}}{3 - \sqrt{13}}$ .

$- \frac{4 (3 - \sqrt{13})}{(3 + \sqrt{13}) (3 - \sqrt{13})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{4 (3 - \sqrt{13})}{9 - 3 \sqrt{13} + \sqrt{13} \cdot 3 - {\sqrt{13}}^{2}}$

Step 5

Simplify.

$- \frac{4 (3 - \sqrt{13})}{- 4}$

Step 6

Simplify the expression.

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Step 6.1

Move the negative one from the denominator of $\frac{3 - \sqrt{13}}{- 1}$ .

$- (- 1 \cdot (3 - \sqrt{13}))$

Step 6.2

Rewrite $- 1 \cdot (3 - \sqrt{13})$ as $- (3 - \sqrt{13})$ .

$- - (3 - \sqrt{13})$

Step 7

Apply the distributive property.

$- (- 1 \cdot 3 - - \sqrt{13})$

Step 8

Multiply $- 1$ by $3$ .

$- (- 3 - - \sqrt{13})$

Step 9

Multiply $- - \sqrt{13}$ .

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Step 9.1

Multiply $- 1$ by $- 1$ .

$- (- 3 + 1 \sqrt{13})$

Step 9.2

Multiply $\sqrt{13}$ by $1$ .

$- (- 3 + \sqrt{13})$

Step 10

Apply the distributive property.

$- - 3 - \sqrt{13}$

Step 11

Multiply $- 1$ by $- 3$ .

$3 - \sqrt{13}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$3 - \sqrt{13}$

Decimal Form:

$- 0.60555127 \dots$