Evaluate 7/(9- square root of 3)

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{7 (9 + \sqrt{3})}{78}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7 (9 + \sqrt{3})}{78}$

Decimal Form:

$0.96313276 \dots$