Are you supposed to perform partial fraction decomposition for a quadratic component that factorizes to rational numbers?

Let’s say you have to spread a cubic equation into partial fraction. What you would normally get is a linear factor and a quadratic or a linear and 2 linears expressions. My question is, for that quadratic factor ,if the solutions are fractions (for example : $ (x + 1/2)(x+2/3) $), then are you supposed to break it down to $ (A)/(x + 1/2) + (B)/(x+2/3) $ ? What i want to know is : if solutions are not whole numbers , do you have to reduce the factor, and why not or why?