1. Objectives: 1.Be able to determine if an equation is a rational equation. 2.Be able to solve various rational equations and exclude any extraneous solutions. Critical Vocabulary: Rational Function, Extraneous solution

2. What is a Rational Equation? In Simple terms, it’s a fraction. 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 I. Rational Functions So, would this equation be rational? No, that would be a linear equation. So, what is a rational then? I think I get it. I bet this is a rational equation. Looks like you got it.

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

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

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

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

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