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2. 7.1 Rational Functions and Simplifying Rational Expressions

3. Rational Expressions Rational expressions can be written in the form where P and Q are both polynomials and Q  0. Examples of Rational Expressions

4. A rational expression is undefined if the denominator is 0. Example: The rational expression is undefined when x = 3. Domains of Rational Functions

5. Are there any values for x for which each rational expression is undefined? The expression is undefined when 15x + 45 = 0. So the expression is undefined when x =  3. Example

6. Find the domain of each rational function. a. b. c. Example

7. Simplifying a rational expression means writing it in lowest terms or simplest form. Simplifying a Rational Expression 1) Completely factor the numerator and denominator. 2) Divide out factors common to the numerator and denominator. (This is the same as “removing a factor of 1.”) Simplifying Rational Expressions

8. Simplify: Example

9. Simplify: Example

10. Simplify: Example

11. Simplify: Example

12. For the ICL Production Company, the rational function describes the company’s cost per disc of pressing x compact discs. Find the cost per disc for pressing a. 100 compact discsb. 1000 compact discs Example a. The cost is $102.60. b. The cost is $12.60.