How to Solve Rational Equations Using the Cross Product

Miacademy & MiaPrep Learning Channel

This instructional math video guides students through the process of solving rational equations using the cross product method. The presenter, Justin, begins by clearly distinguishing between simplifying rational expressions and solving rational equations, emphasizing the role of the equal sign. The video introduces the criteria required to use the cross product method effectively: having only one fraction on each side of the equation and ensuring denominators do not share common factors. The lesson progresses through three distinct examples of increasing complexity. The first example involves basic linear solving and includes a sidebar on proper rounding techniques for decimals. The second example introduces binomials in the denominators, requiring distribution. The final example results in a quadratic equation that must be factored, leading to a critical discussion about extraneous solutions and why the cross product might not always be the most efficient method if denominators share factors. For educators, this video serves as an excellent core lesson or review for Algebra 1 and Algebra 2 units on rational functions. It explicitly addresses common student pitfalls, such as confusing expressions with equations and neglecting to check for extraneous solutions. The step-by-step modeling of problems encourages students to pause and practice, making it a versatile tool for flipped classrooms or independent study.