Solving Rational Equations
Rational equations can be solved using one of two methods:
- Eliminating Denominators This is the same method you learned for solving linear equations:
- factor everything
- multiply both sides by every factor in the denomminators, this should eliminate all the fractions
- solve the resulting polynomial equation
- confirm that none of the solutions from (3) make one of the denominators in the original equation equal to 0
- Combine to a Single Expression This method has the advantage that you don't have to worry about extraneous solutions.
- set the equation equal to 0
- factor everything
- give all the rational expressions a common denominator
- combine the expressions into a single rational expression
- simplify the expression by canceling common factors
- set the numerator equal to 0 and solve to get the final answers
Video Lectures
In this lecture, we're going to see how rational equations can be solved using the method of eliminating the denominators that's the same one you learn for solving linear equations with fractions. We'l also see an example that demonstrates the disadvantage of this method. (lecture slides)
Rational equations can also be solved by combining all the individual expressions into a single rational expression, simplifying the result then setting the numerator equal to 0. This has the disadvantage of being more complicated but you don't have to worry about checking for potential extraneous solutions. (lecture slides)