If are elements of a ring the field of fractions of is the field where the element is written with addition and multiplication defined as in (2) and (1) respectively. This is how the field of rationals is constructed from the ring of integers. If you go along this line, then the results you want to prove are merely definitions of addition and multiplication in the field of fractions, and so there is nothing to prove!
two equivalence classes x/y and z/t becomes: x/y = z/t if and only if xt = yz. i guess they basically want xalk to prove that addition and multiplication defined on Frac(R) is well-defined.