1. Rational Functions and Simplifying Rational Expressions
Section
7.1
Rational Functions and Simplifying Rational Expressions

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

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

4. Example
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.

5. Example
Find the domain of each rational function. Write the domain in set builder notation. a. b. c.

6. Simplifying Rational Expressions
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

7. Example
Simplify:

8. Example
Simplify:

9. Example
Simplify:

10. Example
Simplify:

11. Example
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 discs b compact discs
The cost is $ a. b.
The cost is $12.60. 11