Calculate limit Using Limit Laws

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Homework Statement



Calculate limit Using Limit Laws

Homework Equations



Lim x+2/X^3+8 as X-->(-2)

The Attempt at a Solution




Ok so, I'm a little stumped as to what trick I need to pull out of the bag for this one. Obviously the function goes to 0/0, but I can't seem to factor anything out of the denominator to make it work. But I do know that x to the third and 8 have a cubed root. Any hints or suggestions as to what to do?
 
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What are the limit laws.

Factor x^3 + 8 = ?
And simplify
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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