<p>The mathematical solution for drug concentration over time is a cornerstone of quantitative pharmacology, forming the foundation for optimizing drug use to ensure both efficacy and safety. In this study, we investigated the explicit expression of drug concentration over time in a one-compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination under first-order oral absorption-an open problem in the literature. To address this, we introduce a novel model-to-model approximate approach that enables the analytical expression of drug concentration over time with any desired precision. The developed approximation consists of a sequence of pharmacokinetic sub-models, each possessing a known analytical solution. Notably, these sub-models retain key pharmacokinetic properties, such as distribution, elimination, and total administered dosage. The proposed method is validated through rigorous mathematical proofs and numerical simulations. Compared to existing methods, our approach is more direct and efficient, specifically preserving the mechanistic pharmacology of drug fate while requiring only a small sample size to achieve controllable precision. These findings pave the way for novel advancements in the analysis of pharmacokinetic models, with significant implications for optimizing drug therapy.</p>