1. Quiz 8-3 m < n : y = 0 m = n : y = 1. x-intercepts: (zeroes of numerator) 2. vertical asymptotes: zeroes of denominator 3. horizontal asymptotes: 4. End behavior: y = Find:

2. 8-4: Multiplying and Dividing Rational Expression.

3. Simplifying Rational expressions Expand the numerator and denominators into products of separate fractions. into products of separate fractions. Now simplify = 2 * 1 * y = 2y

4. Your Turn: Simplify:1. 2.

5. Another example Simplify: Expand the numerator and denominators into products of separate fractions. into products of separate fractions.

6. Your Turn: 3. 4.

7. Another Example Look for common factors in numerator and denominator in numerator and denominator

8. Your Turn: 5. Simplify (hint: look for common factors)

9. Multiply then simplify Yuck!

10. BE CAREFUL!!!!! Addition and Subtraction mean: Combine the terms into one term (if you can) No, no, no, no, no!!! If you can’t (unlike terms) they still are connected to each other. Put it into a parentheses.

11. Multiplying Rational Expressions Do you multiply first or do you simplify THEN multiply? Your turn: 6. Simplify the above factored rational expression.

12. Divide Rational Expressions I don’t know how to divide fractions. divide fractions. What do I do? Multiply by the reciprocal Can this fraction be reduced?

13. Dividing Rational Expressions Multiply then simplify OR simplify then multiply?