Topic 5 of 6
Rational Expressions
Track restrictions, simplify factors legally, combine fractions, and solve equations without losing excluded values.
01Algebra · Concept explainerDomain restrictions in rational expressionsA rational expression is undefined wherever its original denominator is zero. Simplifying the formula does not restore an excluded input.02Algebra · Method guideSimplifying rational expressions by factors, not by termsFactor completely, record excluded inputs, and cancel common factors. Individual terms separated by addition cannot be canceled.03Algebra · Method guideAdding and subtracting rational expressionsFactor denominators, build the least common denominator, rewrite every numerator, then combine while preserving restrictions.04Algebra · Method guideSolving rational equations without accepting forbidden answersList restrictions, multiply every term by the least common denominator, solve the resulting equation, and reject candidates outside the original domain.05Algebra · Decision guideDirect or inverse variation: which model matches the relationship?Direct variation keeps a constant ratio y/x; inverse variation keeps a constant product xy. The data pattern decides the model.