Write the Fraction in Simplest Form 3/(2- square root of 7)

$\frac{3}{2 - \sqrt{7}}$

Step 1

Multiply $\frac{3}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

$\frac{3}{2 - \sqrt{7}} \cdot \frac{2 + \sqrt{7}}{2 + \sqrt{7}}$

Step 2

Multiply $\frac{3}{2 - \sqrt{7}}$ by $\frac{2 + \sqrt{7}}{2 + \sqrt{7}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (2 + \sqrt{7})}{4 + 2 \sqrt{7} - 2 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

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

Step 5

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

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

Step 6

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

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

Step 7

Apply the distributive property.

$- 1 \cdot 2 - \sqrt{7}$

Step 8

Multiply $- 1$ by $2$ .

$- 2 - \sqrt{7}$