In the last decades, many families of aggregation functions have been presented playing a fundamental role in many research fields such as decision making, fuzzy mathematical morphology, etc. For this reason, it is necessary to study different types of operators to be potentially used in a concrete application as well as the properties they can satisfy. In this paper, conjunctive and disjunctive rational bivariate aggregation functions of degree two in the numerator and degree one in the denominator are studied. In particular, a characterization of conjunctive and disjunctive rational aggregation functions of degrees (2,1) is presented. Moreover, the symmetry property of these operators are investigated.