This study probes student reasoning with multi-variable expressions in the context of potential difference, ΔV_AB=-W_AB/q_test. Many students reason that if the value of a test charge being moved in an external field between points A and B is increased, the potential difference between the two points is decreased proportionally. It could be argued that these students rely on intuitive ideas informed by their prior practices with similar expressions (e.g., y=a/x) in which a and x represent a constant and a variable, respectively. This automated prior knowledge yields an intuitive mental model based on the assumption that W_AB is a constant, which many accept without giving it a second thought. It is also possible that the knowledge necessary to check for the validity of this assumption is weak or missing. This study is guided by the dual-process theories of reasoning and probes the likely sources of reasoning errors with multi-variable expressions.