2. 3.8 Simplify Rational ExpressionsVocabulary An expression that can be written as a ratio of two polynomials. Rational Expression A number that makes a rational expression undefined. Excluded Value A rational expression when the numerator and denominator have no factors in common other than 1. Simplest form of a rational expression

3. 3.8 Simplify Rational Expressions Example 1 Find excluded values Find the excluded values, if any, of the expression. a.The expression is undefined when ________ = 0, or x = ___, the excluded value is _____.

4. 3.8 Simplify Rational Expressions Example 1 Find excluded values Find the excluded values, if any, of the expression. b.The expression is undefined when ________ = 0, or  ______)(_______) = 0. The solutions to the of the equation are ____ and ____. The excluded values are ____ and ____.

5. 3.8 Simplify Rational Expressions Example 1 Find excluded values Find the excluded values, if any, of the expression. c.The expression is undefined when ________ = 0. The graph of y = x 2 + 2 ________________________. So, the quadratic equation has _____________. does not cross the x-axis no real roots There are ___________________. no excluded values

6. 3.8 Simplify Rational Expressions Checkpoint. Find the excluded values, if any, of the expression.

7. 3.8 Simplify Rational Expressions Example 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. The excluded value is _____.

8. 3.8 Simplify Rational Expressions Example 2 Simplify expressions by dividing out monomials Simplify the rational expression, if possible. State the excluded values. The excluded value is _____.

9. 3.8 Simplify Rational Expressions Checkpoint. Simplify the rational expression, if possible. State the excluded values. Since the expression on the top and bottom cannot be factored, and they do not have any common factors other than 1, the expression is already simplified.

10. 3.8 Simplify Rational Expressions Checkpoint. Simplify the rational expression, if possible. State the excluded values.

11. 3.8 Simplify Rational Expressions Checkpoint. Simplify the rational expression, if possible. State the excluded values.

12. 3.8 Simplify Rational Expressions Example 3 Simplify expressions by dividing out binomials Simplify. State the excluded values. The excluded values are _____ and _____.

13. 3.8 Simplify Rational Expressions Checkpoint. Simplify the rational expression, if possible. State the excluded values.

14. 3.8 Simplify Rational Expressions Checkpoint. Simplify the rational expression, if possible. State the excluded values.

15. 3.8 Simplify Rational Expressions Pg. 178, 3.8 #1-21