#### Answer

$$2r^{2}+3rs-5s^{2}$$

#### Work Step by Step

Initial equation: $$\frac{-8r^{3}s-12r^{2}s^{2}+20rs^{3}}{-4rs}$$
Begin by factoring both the numerator and denominator. In this case, only the numerator factors, and is done so by taking out a GCF of $-4rs$:
$$-4rs(2r^{2}+3rs-5s^{2})$$ Put this back over the denominator:
$$\frac{-4rs(2r^{2}+3rs-5s^{2}}{-4rs}$$ Finally, remove what cancels out to get the final answer:
$$2r^{2}+3rs-5s^{2}$$