Creating equitable performance outcomes among students is a focus of many instructors and researchers. One focus of this effort is examining disparities in physics student performance across genders, which is a well-established problem. Another less common focus is disparities across racial and ethnic groups, which may have received less attention due to low representation rates making it difficult to identify gaps in their performance. In this investigation we examined associations between Learning Assistant (LA) supported courses and improved equity in student performance. We built Hierarchical Linear Models of student performance to investigate how performance differed by gender and by race/ethnicity and how LAs may have moderated those differences. Data for the analysis came from pre-post concept inventories in introductory mechanics courses collected through the Learning About STEM Student Outcomes (LASSO) platform. Our models show that gaps in performance across genders and races/ethnicities were similar in size and increased from pre to post instruction. LA-support is meaningfully and reliably associated with improvement in overall student performance but not with shifts in within-course performance gaps.