How to Rationalize the Numerator and Denominator

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on how to rationalize the numerator of algebraic fractions containing radicals. The instructor guides viewers through three distinct examples, ranging from basic numerical fractions to complex algebraic expressions involving variables in both the numerator and denominator. The video demonstrates the step-by-step process of identifying the conjugate, multiplying the fraction, and simplifying the resulting expression using the FOIL method and algebraic cancellation. The content focuses on key algebraic concepts including conjugates, the difference of squares, expanding binomials containing radicals, and simplifying rational expressions. A specific emphasis is placed on recognizing when terms are additive inverses (opposites) and how to factor out a negative one to facilitate cancellation—a common stumbling block for students. This resource is highly valuable for high school algebra and pre-calculus classrooms, as well as for calculus students reviewing the algebraic skills necessary for evaluating limits. Teachers can use this video to introduce the concept of rationalizing numerators (often counterintuitive to students used to rationalizing denominators) or as a remediation tool for students struggling with radical operations.