Determine all values of x for which f is not defined.
f(x) = (2x^3 + 5x^2 -22x + 15) / (2x^3 + 15x^2 - 34x + 24)
You need to find where the denominator is zero, so the problem becomes how do you find the zeros of
Well, all rational zeros of this polynomial have the form
So your list of possible rational zeros is
Since none of these work you need to resort to something like Cardano's method (very ugly) or numerical approximation. I get that there is one real zero around -9.44.