Question

vertical asymptote of y= (x^4-2x^3+x^2)/(3x^3-9x^2+6x)

Answer 1

factor the numerator ad denominator

cancel any common factors

x^2(x^2 - 2x + 1)/3x(x^2 - 3x + 2)

which then factors to

\[\frac{x^2(x - 1)^2}{3x(x -1)(x-2)}\]

any common factors will be points of discontinuity...

after removing the common factors, what's left in the denominator will help
you get the vertical asymptote.

remember, vertical asymptotes are the values of x that make the denominator zero

Answer 2

so x =2

Answer 3

that's the only vertial asymptote, If you grah the curve using

https://www.desmos.com/calculator

you would see it