Students simplify rational expressions by factoring polynomials, preserving denominator restrictions, and multiplying or dividing by canceling common factors rather than individual terms. They add and subtract rational expressions by finding a least common denominator, combining numerators correctly, and working with linear or common quadratic factors. They determine valid domains, solve simple rational equations by clearing denominators, reject extraneous solutions through checks in the original equation, and interpret rational expressions as rates, proportions, or relationships in context.