1. Rational Function, Extraneous (excluded values) solutions
Objectives:
Be able to solve various rational equations and exclude any extraneous solutions.
Critical Vocabulary:
Rational Function, Extraneous (excluded values) solutions

2. Solving Rational Equations
1st Choose the appropriate method (Cross Multiply or Multiply by LCD).
Simplify and solve the equation.

3. I. Solving Rational Equations
a. Solving a Rational: Cross Multiplication (Proportion) 1.
First determine what “x” can’t be
(6t + 7)(2t - 4) = (4t - 1)(3t + 8)
Cross Multiply
12t2 - 10t - 28 = 12t2 + 29t - 8
FOIL
-10t - 28 = 29t - 8
What are talking about? What is an extraneous solution?
-39t - 28 = -8
-39t = 20
Solution: x = -20/39
That’s where your solution is one of the values that “x” can’t be.
Look like you didn’t get any extraneous solutions.

4. Ex. 2

5. You try! Solve.

6. This is not an extraneous solution either.
II. Solving Rational Equations
Method 2: Solving a Rational: By Finding LCM (Denominator) 2.
What can x not be?
Multiply by LCD
Distribute
6 + 8x = 7
8x = 1
This is not an extraneous solution either.
Solution: x = 1/8
No….really?

7. Let’s Practice #1 Solve.

8. #2 Solve.

9. Now, you do these on your own.

10. 3. II. Solving Rational Equations What can x not be? Multiply by LCD
3x + 2(x - 1) = 3
Distribute
3x + 2x - 2 = 3
This means there is no solution
5x - 2 = 3
5x = 5
x = 1
This is extraneous. What does that mean?
Solution: None

11. #5 Solve.

12. Homework! Copy each Add or Subtract. Simplify.

13. II. Solving Rational Equations4.
Factor Denominators
2x = 4 - (x - 2)
2x = 4 - x + 2
3x = 6
x = 2
Solution: None