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Rational Function, Extraneous solution

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

2 II. 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.

3 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?

4 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

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


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