Question 771271
{{{(x^2+x-12)/(x+2)}}} fully factorable to 
{{{(x-3)(x+4)/(x+2)}}}


Performing polynomial division of the expression in the originally given form, the quotient will be {{{x-1-10/(x+2)}}}, giving a slant asymptote of {{{y=x-1}}}.   Vertical asymtpote is at {{{x=-2}}} becasue the denominator must not be zero  (the denominator of the given expression).


Two zeros occur:  x=-4, and x=3 are the zeros of the function.  


Critical points are x at -4, -2, and 3.  These are the intervals along the horizontal axis.  ...
{{{x<-4}}}
{{{-4<x-2}}}
{{{-2<x<3}}}
{{{3<x}}}
What you want to do is test any x value in each interval and find if the function is positive or negative.  I omit that part of the analysis, but this is the graph:


{{{graph(400,400,-8,8,-8,8,(x^2+x-12)/(x+2))}}}


OR THIS


{{{graph(500,500,-15,15,-15,15,(x^2+x-12)/(x+2))}}}