Di-hadron correlations and jet-hadron correlations are frequently used to study interactions of the Quark Gluon Plasma with the hard partons that form jets. The existing background subtraction methods for these studies depend on several assumptions and independent measurements of the Fourier coefficients of the combinatorial background. In this paper, we present two background subtraction methods which use the observation that the near-side correlation signal is negligible for large separations

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... between the associated particle and the trigger. The combinatorial background is fit in this background-dominated region. Including the reaction plane dependence of the raw correlation improves these results. To test the accuracy of these methods, a simple model is used to simulate di-hadron and jet-hadron correlations with a combinatorial background similar to that observed in the data. The true signal is compared to the extracted signal. The results are compared to results from two variants of the Zero-Yield-At-Minimum (ZYAM) method. We test these methods for mid-peripheral and central collisions and for di-hadron and jet-hadron correlations. These methods are more precise than the ZYAM method with fewer assumptions about the shape and level of the combinatorial background, even in central collisions where the experimental resolution on the measurement of the reaction plane dependence is poor. These methods will allow more accurate studies of modifications of the away-side jet and will be particularly useful for studies of jet-hadron correlations, where the combinatorial background is poorly constrained from previous studies.