Simplify 9/(2- square root of 7)

$\frac{9}{2 - \sqrt{7}}$

Step 1

Multiply $\frac{9}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

$\frac{9}{2 - \sqrt{7}} \cdot \frac{2 + \sqrt{7}}{2 + \sqrt{7}}$

Step 2

Multiply $\frac{9}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

$\frac{9 (2 + \sqrt{7})}{(2 - \sqrt{7}) (2 + \sqrt{7})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (2 + \sqrt{7})}{4 + 2 \sqrt{7} - 2 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{9 (2 + \sqrt{7})}{- 3}$

Step 5

Cancel the common factor of $9$ and $- 3$ .

Factor $3$ out of $9 (2 + \sqrt{7})$ .

$\frac{3 (3 (2 + \sqrt{7}))}{- 3}$

Move the negative one from the denominator of $\frac{3 (2 + \sqrt{7})}{- 1}$ .

$- 1 \cdot (3 (2 + \sqrt{7}))$

Step 6

Rewrite $- 1 \cdot (3 (2 + \sqrt{7}))$ as $- (3 (2 + \sqrt{7}))$ .

$- (3 (2 + \sqrt{7}))$

Step 7

Apply the distributive property.

$- (3 \cdot 2 + 3 \sqrt{7})$

Step 8

Multiply $3$ by $2$ .

$- (6 + 3 \sqrt{7})$

Step 9

Apply the distributive property.

$- 1 \cdot 6 - (3 \sqrt{7})$

Step 10

Multiply.

Multiply $- 1$ by $6$ .

$- 6 - (3 \sqrt{7})$

Multiply $3$ by $- 1$ .

$- 6 - 3 \sqrt{7}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- 6 - 3 \sqrt{7}$

Decimal Form:

$- 13.93725393 \dots$