Is there a way to find "polynomial rational functions" having point of inflections, in their graphs?

For example if the derivative of f(x) is

${f}^{\prime}(x)=\frac{(x-1{)}^{2}(x-3)}{(x-2)}$

then f(x) has a point of inflection at $x=1$.

But f(x) is not a polynomial rational !

Is there a way to determine which antiderivatives are the ratio of to polynomials?

For example if the derivative of f(x) is

${f}^{\prime}(x)=\frac{(x-1{)}^{2}(x-3)}{(x-2)}$

then f(x) has a point of inflection at $x=1$.

But f(x) is not a polynomial rational !

Is there a way to determine which antiderivatives are the ratio of to polynomials?