Solving Rational Equations
- A rational equation is an equation
containing one or more rational expressions (usually one
of these has a variable in the denominator).
- There are two things to watch for in the procedure below.
- It’s the fractions that make a rational equation
look scary. Thus, the first part of the procedure below
acts to eliminate the fractions.
- We have to remember that certain numbers make a rational
expression undefined. Those numbers CANNOT be solutions,
so the last part of the procedure below checks to make
sure that none of our “solutions” are BAD
numbers.
Procedure: (Solving a Rational Equation)
1. Eliminate the fractions from the equation as follows:
- Find the LCD of all fractions (on BOTH sides of the
“=”).
- Multiply each term by the LCD (over 1), REGARDLESS OF
WHETHER THAT TERM IS A FRACTION OR NOT!!
2. Solve the resulting equation.
3. Check the solutions found in step 2 to make sure that they
do not make any of the denominators 0. Throw any that do out.
