Answer
$$-3rs-r+2s$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{9r^2s^2+3r^2s-6rs^2}{-3rs} \\ -\left(3rs+r-2s\right)\\ -3rs-r+2s$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.