Simplify 4/(3- square root of 11)

$\frac{4}{3 - \sqrt{11}}$

Step 1

Multiply $\frac{4}{3 - \sqrt{11}}$ by $\frac{3 + \sqrt{11}}{3 + \sqrt{11}}$ .

$\frac{4}{3 - \sqrt{11}} \cdot \frac{3 + \sqrt{11}}{3 + \sqrt{11}}$

Step 2

Multiply $\frac{4}{3 - \sqrt{11}}$ by $\frac{3 + \sqrt{11}}{3 + \sqrt{11}}$ .

$\frac{4 (3 + \sqrt{11})}{(3 - \sqrt{11}) (3 + \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (3 + \sqrt{11})}{9 + 3 \sqrt{11} - 3 \sqrt{11} - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{4 (3 + \sqrt{11})}{- 2}$

Step 5

Cancel the common factor of $4$ and $- 2$ .

Factor $2$ out of $4 (3 + \sqrt{11})$ .

$\frac{2 (2 (3 + \sqrt{11}))}{- 2}$

Move the negative one from the denominator of $\frac{2 (3 + \sqrt{11})}{- 1}$ .

$- 1 \cdot (2 (3 + \sqrt{11}))$

Step 6

Rewrite $- 1 \cdot (2 (3 + \sqrt{11}))$ as $- (2 (3 + \sqrt{11}))$ .

$- (2 (3 + \sqrt{11}))$

Step 7

Apply the distributive property.

$- (2 \cdot 3 + 2 \sqrt{11})$

Step 8

Multiply $2$ by $3$ .

$- (6 + 2 \sqrt{11})$

Step 9

Apply the distributive property.

$- 1 \cdot 6 - (2 \sqrt{11})$

Step 10

Multiply.

Multiply $- 1$ by $6$ .

$- 6 - (2 \sqrt{11})$

Multiply $2$ by $- 1$ .

$- 6 - 2 \sqrt{11}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- 6 - 2 \sqrt{11}$

Decimal Form:

$- 12.63324958 \dots$