Simplify -3/( square root of 7-9)

$\frac{- 3}{\sqrt{7} - 9}$

Step 1

Move the negative in front of the fraction.

$- \frac{3}{\sqrt{7} - 9}$

Step 2

Multiply $\frac{3}{\sqrt{7} - 9}$ by $\frac{\sqrt{7} + 9}{\sqrt{7} + 9}$ .

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

Step 3

Multiply $\frac{3}{\sqrt{7} - 9}$ by $\frac{\sqrt{7} + 9}{\sqrt{7} + 9}$ .

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{3 (\sqrt{7} + 9)}{{\sqrt{7}}^{2} + \sqrt{7} \cdot 9 - 9 \sqrt{7} - 81}$

Step 5

Simplify.

$- \frac{3 (\sqrt{7} + 9)}{- 74}$

Step 6

Move the negative in front of the fraction.

$- - \frac{3 (\sqrt{7} + 9)}{74}$

Step 7

Multiply $- - \frac{3 (\sqrt{7} + 9)}{74}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{3 (\sqrt{7} + 9)}{74}$

Multiply $\frac{3 (\sqrt{7} + 9)}{74}$ by $1$ .

$\frac{3 (\sqrt{7} + 9)}{74}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (\sqrt{7} + 9)}{74}$

Decimal Form:

$0.47212505 \dots$