Final answer:
The correct answer is hepatic metabolism and renal excretion, where drugs are metabolically transformed in the liver and excreted through the kidneys via urine.
Step-by-step explanation:
The major routes that remove etomidate and midazolam from the body are hepatic metabolism and renal excretion. These drugs are metabolically transformed in the liver, which is a process that includes oxidation, reduction, and hydrolysis, followed by phase II reactions like conjugation. This prepares them for excretion. Subsequently, the metabolites, now rendered more water-soluble, are primarily excreted through the kidneys via urine. Some components may also be secreted into the bile and eliminated through feces. Water-soluble drugs are influenced by glomerular filtration, tubular secretion, or tubular reabsorption in the renal system. Therefore, the correct answer to the question is A. hepatic metabolism and renal excretion.