Lim x^2 - 2x - 15/x^2-9

5/3 if x → 0, 1 if x → ∞

Step-by-step explanation:

I'm going to answer this for two potential scenarios: the limit as x approaches 0, and the limit as x approaches infinity. First, let's factor and simplify our expression a little. factors into , and is the difference of squares , so we can factor it into . Our expression now becomes

If we take the limit of this as x → 0:

And the limit as x → ∞:

An explanation for that second limit: As x gets larger and larger, the 5 and 3 being subtracted in the numerator and denominator become less and less significant, and the fraction gets closer and closer to the value x/x, which is 1.