Rational Function, Extraneous (excluded values) solutions

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Solving Rational Equations

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Presentation transcript:

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

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

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.

Ex. 2

You try! Solve.

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?

Let’s Practice #1 Solve.

#2 Solve.

Now, you do these on your own.

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 Solve.

Homework! Copy each Add or Subtract. Simplify.

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