How to Add and Subtract Rational Expressions with Unlike Denominators

The Organic Chemistry Tutor

This comprehensive math tutorial guides students through the process of adding and subtracting rational expressions with unlike denominators. The video progresses from basic examples with monomial denominators to complex problems requiring the factoring of quadratic equations. It emphasizes the critical steps of finding the Least Common Denominator (LCD), adjusting numerators, distributing negative signs, and simplifying the final result. The content explores key algebraic themes including finding the Least Common Multiple (LCM) for algebraic terms, factoring trinomials, the difference of squares, and the specific technique of factoring out a negative one to align denominators. A major focus is placed on algebraic manipulation, specifically the 'FOIL' method for expanding binomials and factoring by grouping for cubic polynomials. For educators, this video serves as an excellent instructional tool for Algebra II or Pre-Calculus units. It is particularly valuable for its scaffolded approach, starting simple and building complexity. The clear, step-by-step visual working of problems allows teachers to pause for student practice or use specific segments to address common pain points, such as sign errors when subtracting entire rational expressions.