Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$- \frac{12 \cdot \left(1 + \frac{2 x - 3}{x - 3} - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right)}{x^{2} \left(x - 3\right)} = 0$$
Solve this equationSolutions are not found,
maybe, the function has no inflections