Question

Any help would be really appreciated!

Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.

A: -3 - 6i/5
B: 39 - 6i/-9
C: -39 - 6i/ 17
D: 3 - 6i/3

(The first pic attached is the actual equation and the next are the potential answers)

Answer 1

$\frac{\sqrt{-9}}{(4-7i)-(6-6i)}=\\ \frac{\sqrt{9*i^2}}{-2-i}=\\ \frac{3i}{-2+i}*\frac{-2+i}{-2+i}=\\ \frac{3i*(-2+i)}{(-2-i)*(-2+i)}=\\ \frac{-6i+3i^2}{4-i^2}=\\ \frac{-3-6i}{4+1}=\\ \frac{-3-6i}{5}$

so it is the first option