The vertical asymptotes of ##y=(x^2+1)/(3x-2x^2)## are ##x=0## and ##x=3/2##.
To find the vertical asymptotes we set the denominator equal to zero.
Look at the graph below.
Sometimes, the denominator is equal to zero at the same x-value that makes the numerator zero. This will produce a instead of a vertical asymptote.