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**Krizalid** First, note that $\displaystyle x^2+4x-32<0\iff(x-4)(x+8)<0$

Now you have to analyze two possibilities:

$\displaystyle \blacktriangleright~(x-4)>0~~\wedge~~(x+8)<0$

$\displaystyle \blacktriangleright~(x-4)<0~~\wedge~~(x+8)>0$

After, find the intersection of the first one and do the same for the second one. Finally, the intervals that you'll have, join them and that's the answer.

Apply the same idea with the next exercise, but remember that you cannot take the denominator equal to 0.