How to Divide Algebraic Fractions

The Organic Chemistry Tutor

This video tutorial provides a step-by-step guide on how to divide algebraic fractions involving variables, exponents, and polynomials. The instructor introduces the fundamental "Keep, Change, Flip" method used for dividing fractions and demonstrates how to transform division problems into multiplication problems. The video progresses from simple monomial fractions to more complex rational expressions that require factoring before simplification. Key mathematical themes explored include the properties of exponents, prime factorization of integers to aid in cancellation, and factoring binomials using the greatest common factor (GCF). The instructor places heavy emphasis on the strategy of expanding terms (e.g., writing x^3 as x·x·x) to visually demonstrate exactly which variables cancel out, making the abstract rules of exponents concrete and understandable for learners. This resource is highly valuable for Algebra 1 and 2 classrooms as both an introduction to rational expressions and a review of fraction operations. The clear, handwritten derivations allow students to follow the logical flow of simplifying complex expressions. Teachers can use the specific examples to scaffold learning, starting with basic variable cancellation and moving toward problems that integrate factoring skills, helping students build confidence in handling multi-step algebraic procedures.