Simplify (3- square root of -9)/(2- square root of -1)

$\frac{3 - \sqrt{- 9}}{2 - \sqrt{- 1}}$

Pull out imaginary unit $i$ .

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{3 - \sqrt{- 1 (9)}}{2 - \sqrt{- 1}}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\frac{3 - (\sqrt{- 1} \cdot \sqrt{9})}{2 - \sqrt{- 1}}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{3 - (i \cdot \sqrt{9})}{2 - \sqrt{- 1}}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{3 - (i \cdot \sqrt{9})}{2 - i}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{3 - i \cdot \sqrt{3^{2}}}{2 - i}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3 - i \cdot 3}{2 - i}$

Multiply $3$ by $- 1$ .

$\frac{3 - 3 i}{2 - i}$