CALC
posted by UCI .
f(x)=x^33x^23x8/(3x^24x6)
Find the equation of the nonvertical asymptote.
What is the smallest value of x at which f(x) intersects its nonvertical asymptote?
the non vertical asymptote is 1/3x + 13/9 i found that using synthetic division and i know there is an intersect its nonvertical asymptote but i don't know how to find it....

I agree on the asymptote.
So set the intercepts equal..
x/3+ 13/9= (x^33x^23x8)/(3x^24x6)
+x^3 +4x^2/3+2x13/3 x^2 52/9x26/3=x^33x^23x8
combining terms
x^2 (4/313/3+3) +x(2+3 52/9)26/3+8=0
check that several times. then use the quadratic equation to solve for x