Question 320132
{{{Q(x) = (4x + 7x^2) / (x^2-7x + 12)}}}
{{{Q(x)=(x(4x+7))/((x-3)(x-4))}}}
There are two vertical asymptotes, when the denominator equals zero:
{{{x-3=0}}}
{{{x=3}}}
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{{{x-4=0}}}
{{{x=4}}}
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{{{Q(x) = (4x + 7x^2) / (x^2-7x + 12)}}}
{{{Q(x) = ((4x)/(x^2) + (7x^2)/(x^2)) / ((x^2)/(x^2)-(7x)/(x^2) + 12/(x^2))}}}
{{{Q(x) = (4/x + 7) / (1-7/x + 12/x^2)}}}
{{{lim(x->infinity,Q(x))=((0+7)/(1-0+0))=7}}}
The horizontal asymptote is {{{y=7}}}.