How to calculate this limit?

Because plugging in zero leaves us with n/0, we can determine that the limit as x→0 will be either ∞, -∞, or DNE. Next, we can plug in positive and negative values to see if it is decreasing or increasing on either side. Using negative values, we can determine that from the left the limit is -∞ as it is decreasing. Using positive values, we can determine that from the right the limit is -∞ as it is decreasing. As our right and left limits match, we can determine the limit from both sides is -∞.