Answer
slant $y=x+1$
vertical $x=-2, x=2$
Work Step by Step
Use long division and factor the denominator to get
$r(x)=x+1+\frac{4x+4}{(x+2)(x-2)}$
so we can identify the asymptotes as
slant $y=x+1$
vertical $x=-2, x=2$
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