Using a very recent approach based on the Charnes-Cooper trasformation we characterize the pseudoconvexity of the sum between a quadratic fractional function and a linear one. Furthemore we prove that the ratio between a quadratic fractional function and the cube of an affine one is pseudoconvex if and only if the product between a quadratic fractional function and an affine one is pseudoconvex and we provide a sort of canonical form for this latter class of functions. Benefiting by the new results we\ are able to characterize the pseudoconvexity of the ratio between a quadratic fractional function and the cube of an affine one.