We can see that the (x+3) factor is causing the problem if we directly evaluated the limit by plugging in x = -3. So, let's

**assume** that the numerator is divisible by (x+3) so that

the (x+3)'s will cancel and all that remains is to plug in x = -3 directly.

So, we do long division and you should get the remainder:

Since we want (x+3) to factor in nicely, we can assume that the remainder is 0. i.e.

So we have:

You know where to go from there

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Or if you learned l'hopital's, you could go that route and set the numerator equal to 0 and solve for a. Then differentiate and solve the limit.