1 / 12

Rational Expressions and Equations

Rational Expressions and Equations. Chapter 6. § 6.1. Simplifying, Multiplying, and Dividing. A rational expression is an expression of the form where P and Q are polynomials and Q is not 0. Fractional algebraic expression. x  – 5. Rational Expressions. or.

keown
Télécharger la présentation

Rational Expressions and 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. Rational Expressions and Equations Chapter 6

  2. § 6.1 Simplifying, Multiplying, and Dividing

  3. A rational expression is an expression of the form where P and Q are polynomials and Q is not 0. Fractional algebraic expression x – 5 Rational Expressions or A function defined by a rational expression is a rational function. The domain of a rational function is the set of values that can be used to replace the variable.

  4. Simplifying by Factoring Example: Find the domain of x2 – 2x – 8 = 0 Set the denominator equal to 0. (x + 2)(x – 4) = 0 Factor. x + 2 = 0 or x – 4 = 0 Use the zero factor property. x = – 2 x = 4 Solve for x. The domain of y = f(x) is all real numbers except – 2 and 4.

  5. Example: Reduce. Basic Rules of Fractions Basic Rules of Fractions For any polynomials a, b, or c, where band c  0.

  6. Simplifying by Factoring Example: Simplify. Factor 5 from the numerator. Apply the basic rule of fractions.

  7. Remember that when a negative number is factored from a polynomial, the sign of each term in the polynomial changes. Simplifying by Factoring Example: Simplify. Factor –2 from the numerator. Apply the basic rule of fractions.

  8. Simplifying by Factoring Example: Simplify. Factor x from the numerator. Factor the numerator. Factor the denominator. Apply the basic rule of fractions.

  9. Multiplying Rational Expressions For any polynomials a, b, c, and d, where band d  0. Rational expressions may be multiplied and then simplified. Rational expressions may also first be simplified and then multiplied. 7 1 5 1 This method is usually easier.

  10. Simplifying the Product Example: Multiply. Factor each numerator and denominator. Factor again whenever possible. Apply the basic rule of fractions.

  11. Example: Divide. Dividing Rational Expressions The definition for division of fractions is Invert the second fraction and multiply. This is called the reciprocal. 2 Apply the basic rule of fractions.

  12. Simplifying the Quotient Example: Divide. Invert the second fraction and multiply. Factor the numerator and denominator. Apply the basic rule of fractions.

More Related