The vertical asymptotes of a curve are lines that the graph of the curve approaches but does not touch.
For `y = (f(x))/(g(x))` , the vertical asymptotes are lines x = a where a is the root of the denominator g(x).
The equation of the curve in the problem is `y = (1 + x^2)/(3x - 2x^2)`
To determine the roots of the denominator solve 3x - 2x^2 = 0
x(3 - 2x) = 0
x = 0, x = 3/2
The roots of the denominator are x = 0 and x = 3/2.
The vertical asymptotes of the curve `(1 + x^2)/(3x - 2x^2) ` are x = 0 and x = 3/2.
This can be verified by looking at the graph of the curve: