Where R notes resitivity, Rxyoh represents the Rxy part coming form the ordinary Hall effect.
A good discussion of anomalous hall conductivity in thin film is given in the book "modern magnetic materials principles and applications " [http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471155667.html] . Perhaps that can help u
Also when u consider the actual hall effect measurements, you typically to measure the resistance(or voltage ) vs magnetic field. So even if u are measuring what u think is hall resistance (or hall voltage), you end up measuring longitudinal resistance + hall resistance, resistances which are typically in paralle. This is because there is always a small mismatch between the hall contacts.
So actually you have resistances (ordinary resistances and hall resistances) that are in parallel (i.e conductivities that are in series), so if u invert your formula, the first part is square of longitudinal resistance divided by hall resistance, which is a big number(because Rxx >>> Rxy ~ 1000 times higher) while the second term is square of hall resistance divided by hall resistance, a smaller term. So now if u look at this when it is inverted (as in your formula), the first term has minimal contribution, because the denominator is high and the second term has more contribution.
hope this helps
You may consult the nice eview article by N. Nagaosa et al. in arXiv:0904.4154v1.
It is now known that the Hall conductance under a electric field and a perpendicular magnetic field should be expressed into -Rxy/(Rxx^2+Rxy^2) , and anamolus hall conductance so should be -Rxy(AH)/(Rxx^2+Rxy^2) .
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