Question 352559
{{{y= (x^2+3x+2)/(x^3+4x^2-3x-18)}}}
{{{y= ((x+1)(x+2))/((x-3)(x+2)^2)}}}
{{{y= ((x+1))/((x-3)(x+2))}}}
Vertical asymptotes at {{{x=3}}} and {{{x=-2}}}.
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{{{((x+1))/((x-3)(x+2))=0}}}
{{{x+1=0}}}
{{{x=-1}}}
X-intercept is ({{{-1}}},{{{0}}}).
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{{{y= ((x+1))/((x-3)(x+2))}}}
{{{y= ((0+1))/((0-3)(0+2))}}}
{{{y=-1/6}}}
Y-intercept is ({{{0}}},{{{-1/6}}})
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{{{y= (x^2+3x+2)/(x^3+4x^2-3x-18)}}}
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{{{y= (x^2/x^3+3x/x^3+2/x^3)/(x^3/x^3+4x^2/x^3-3x/x^3-18/x^3)}}}
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{{{y= (1/x+3/x^2+2/x^3)/(1+4/x-3/x^2-18/x^3)}}}
As {{{x->infinity}}}, 
{{{y= (0+0+0)/(1+0-0-0)}}}
{{{y->0}}}
As {{{x->-infinity}}}, {{{y->0}}}
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{{{drawing(300,300,-10,10,-5,5,blue(line(-2,10,-2,-10)),blue(line(3,10,3,-10)),grid(1),graph(300,300,-10,10,-5,5,((x+1)(x+2))/((x-3)(x+2)^2)))}}}