In this final lecture on Rational Equations, Dr. Eaton first begins with the definition of rational equations and moves into cross multiplications in solving rational equations. She covers how to solve any rational equation by multiplying by the LCM of the denominators. After a thorough investigation of work problems she ends the lecture with extraneous solutions and how you must check all solutions.
A rational equation is an equation that contains rational expressions.
To solve a rational equation, multiply each term on both sides by the LCM of all the denominators in the equation. Then solve the resulting equation, which has no fractions.
An extraneous solution is a value that makes one or more of the denominators in the original equation equal to 0. Always check all potential solutions in the original equation. Exclude extraneous values from the solution set.
Here is a better way to deal with extraneous solutions: before solving the equation, determine the values that must be excluded by setting each denominator equal to 0 and solving. Then you will recognize an extraneous solution as soon as it appears as a possible solution.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.