1. Solving Rational Equations
Section 6.6
Solving Rational Equations

2. Definition A rational equation is an equation that contains
one or more rational expressions.
Examples:
Goal: Clear Fractions

3. Solving Rational Equations
1) Factor each denominator completely to find LCD
2) Multiply both sides by the LCD to clear the fractions
3) Solve the resulting equation
4) Check all possible solutions in the original equation

4. Example Solve the equation 1 Multiply both sides by the LCD 7 3 1
LCD is
21x
21x
21x
21x 1 1 1
Solve the resulting equation

5. Example Solve 1 Multiply both sides by the LCD 1 1 1 LCD is 5b 5b 5b
Solve the resulting equation
Check the solution in the original equation

6. Example Solve the equation Multiply both sides by the LCD 1 1 (q+5)
LCD is
(q+5)
(q+5)
(q+5) 1 1
Solve the resulting equation
No Solution

7. More Examples
Solve the following equations

8. Solving for a specified variable
Isolate the specified variable in a formula
The answer is another formula (not a numerical value)

9. Example Solve for R Multiply both sides by the LCD 1 LCD is (R+r)
NO!
Subtracting rI on both sides
Dividing both sides by I

10. Example Solve for b 1 Multiply both sides by the LCD 1 1 1 abf LCD is
Solve the resulting equation
Move the term containing b to the left
Factor out common factor b
Divide both sides by f – a

11. More Examples
Solve the following equations