In this final lecture on Rational Equations, Dr. Fraser first begins with the definition of rational equations and moves into cross multiplications in solving rational equations. He covers how to solve any rational equation by multiplying by the LCM of the denominators. After a thorough investigation of work problems he ends the lecture with extraneous solutions and how you must check all solutions.
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.
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.
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.