1 / 11

Section 6.4 Rational Equations

Section 6.4 Rational Equations. Solving Rational Equations Clearing Fractions in an Equation Restricted Domains (and Solutions) The Principle of Zero Products The Necessity of Checking Rational Equations and Graphs. A Rational Equation in One Variable May Have Solution(s).

king
Download Presentation

Section 6.4 Rational Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 6.4 Rational Equations • Solving Rational Equations • Clearing Fractions in an Equation • Restricted Domains (and Solutions) • The Principle of Zero Products • The Necessity of Checking • Rational Equations and Graphs 6.4

  2. A Rational Equation in One VariableMay Have Solution(s) • A Rational Equation contains at least one Rational Expression. Examples: • All Solution(s) must be tested in the Original Equation 6.4

  3. False Solutions • Warning: Clearing an equation may add a False Solution • A False Solution is one that causes an untrue equation, or a divide by zero situation in the original equation • Before even starting to solve a rational equation, we need to identify values to be excluded • What values need to be excluded for these? • t ≠ 0 a ≠±5 x ≠ 0 6.4

  4. Clearing Factions from Equations • Review: Simplify- Clear a Complex Fraction by • Multiplying top and bottom by the LCD • Solve - Clear a Rational Equation by • Multiplying both sides by the LCD • Then solve the new polynomial equation using the principle of zero products 6.4

  5. The Principle of Zero Products • Covered in more detail in Section 5.8 • When a polynomial equation is in formpolynomial = 0you can set each factor to zero to find solution(s) • Example – What are the solutions to: • x2 – x – 6 = 0 • (x – 3)(x + 2) = 0 • x – 3 = 0  x = 3 and x + 2 = 0  x = -2 6.4

  6. Clearing & Solving a Rational Equation What gets excluded? x ≠ 0 What’s the LCD? 15x What’s the solution? 6.4

  7. A Binomial Denominator What gets excluded? x ≠ 5 What’s the LCD? x – 5 What’s the solution? 6.4

  8. Another Binomial Denominator What gets excluded? x ≠ 3 What’s the LCD? x – 3 What’s the solution? x = -3 (x = 3 excluded) 6.4

  9. Different Binomial Denominators What gets excluded? x ≠ 5,-5 What’s the LCD? (x – 5)(x + 5) What’s the solution? x = 7 6.4

  10. Functions as Rational Equations What gets excluded? x ≠ 0 What’s the LCD? x What’s the solution? x = 2 and x = 3 6.4

  11. What Next? • 6.5Solving Applications of Rational Equations 6.4

More Related