2. Slide 1- 1 Sum, Difference, Product, and Quotient

4. ©1999 by Design Science, Inc. 3 Example 3 Evaluate and : – You can see that function composition is not commutative!

6. Complex fractions

7. Objective Simplify complex fractions Lets Review fraction rules first…………..

8. Simplifying Complex Fractions A complex fraction is one that has a fraction in its numerator or its denominator or in both the numerator and denominator. Example:

9. Adding/Subtracting Fractions 7 12 = 5 2 + Add. 5 12 2 +

10. Common Denominators 1.Add or subtract the numerators. 2.Place the sum or difference of the numerators found in step 1 over the common denominator. 3.Simplify the fraction if possible. Subtract

11. Common Denominators a.)Add Example:

12. Common Denominators b.) Subtract Example:

13. Unlike Denominators 1.Determine the LCD. 2.Rewrite each fraction as an equivalent fraction with the LCD. 3.Add or subtract the numerators while maintaining the LCD. 4.When possible, factor the remaining numerator and simplify the fraction.

14. Unlike Denominators a.) The LCD is w(w+2). Example:

15. Unlike Denominators b.) The LCD is 12x(x – 1). This cannot be factored any further. Example: