The vertical asymptotes of a function f(x) = A/B are the lines with equation x = a, where a is the roots of the denominator B.
For the function f(x) = (x^2 + 1)/(3x - 2x^2), the denominator is 3x - 2x^2.
The roots of 3x - 2x^2 are the solutions of the equation
3x - 2x^2 = 0
x(3 - 2x) = 0
x = 0 and x = 3/2
The vertical asymptotes of the function are x = 0 and x = 3/2.
The graph of the function verifies the same.
to get the vertical symptotes just equate the denominator to zero.
that is 3x-2x^2=0
the vertical asympoyes are x=0 and x=3/2