Solving Rational Equations Using the LCM Method

Miacademy & MiaPrep Learning Channel

This video provides a comprehensive tutorial on solving rational equations using the Least Common Multiple (LCM) method. It begins by contrasting this approach with the cross-product method, helping students identify exactly when the LCM method is more efficient—specifically when equations involve multiple fractions on one side or share common factors in the denominators. The presenter, Justin, guides viewers through four distinct examples that increase in complexity, demonstrating how to factor denominators, determine the LCM, clear fractions by multiplying, and solve the resulting linear or quadratic equations. The content emphasizes procedural fluency and the critical step of checking for extraneous solutions. By revisiting a problem from a previous lesson, the video highlights how choosing the correct method can simplify the solving process. It covers key algebraic skills including factoring quadratics, distributing terms, combining like terms, and identifying domain restrictions that result in extraneous solutions (division by zero). For educators, this resource serves as an excellent direct instruction tool for Algebra I or Algebra II classes. It models mathematical thinking by asking "which method is best?" before solving. The clear visual breakdown of cancelling factors helps demystify why multiplying by the LCM works. The video is particularly useful for addressing the common student struggle of dealing with complex rational expressions and reinforces the importance of verifying answers in the context of the original equation.