1. Rational Function, Extraneous solution
Objectives:
Be able to determine if an equation is a rational equation.
Be able to solve various rational equations and exclude any extraneous solutions.
Critical Vocabulary:
Rational Function, Extraneous solution

2. Formal Definition: A rational Function is a ratio of two
I. Rational Functions
A rational equation is an equation that contains rational expressions (x in the denominator)
Formal Definition: A rational Function is a ratio of two
polynomials written in the form
No, that would be a linear equation.
Looks like you got it.
I think I get it. I bet this is a rational equation.
What is a Rational Equation?
In Simple terms, it’s a fraction.
So, would this equation be rational?
So, what is a rational then?

3. II. Solving Rational Equations
a. Solving a Rational: Cross Multiplication (Proportion) 1.
First determine what “x” can’t be
(6x + 7)(2x - 4) = (4x - 1)(3x + 8)
Cross Multiply
12x2 – 10x - 28 = 12x2 + 29x - 8
FOIL
-10x - 28 = 29x - 8
What are talking about? What is an extraneous solution?
-39x - 28 = -8
-39x = 20
Solution: x = -20/39
That’s where your solution is one of the values that “x” can’t be.
Looks like you didn’t get any extraneous solutions.

4. This is not an extraneous solution either.
II. Solving Rational Equations
b. 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?

5. 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?
No Solution

6. II. Solving Rational Equations4.
Factor Denominators
2x = 4 - (x - 2)
2x = 4 - x + 2
3x = 6
x = 2
No Solution

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