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

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (\sqrt{3} - \sqrt{7})}{{\sqrt{3}}^{2} - \sqrt{21} + \sqrt{21} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{9 (\sqrt{3} - \sqrt{7})}{- 4}$

Step 5

Move the negative in front of the fraction.

$- \frac{9 (\sqrt{3} - \sqrt{7})}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{9 (\sqrt{3} - \sqrt{7})}{4}$

Decimal Form:

$2.05582613 \dots$