1. 9.1 Multiplying and Dividing Rational Expressions
Complex fractions

2. Definition of a Rational Expression
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions.

3. Since they are fractions
Simplify a Rational Expression.
Divide the same expression from numerator and denominator

4. Since they are fractions
Simplify a Rational Expression.
Divide the same expression from numerator and denominator

5. Since they are fractions
There are numbers that will not work in the Rational expression.
They are -7, 3 and -3. Why?

6. Since they are fractions
Factor out the denominator.
Can you see why -7, 3 and -3 do not work as answers?

7. Since they are fractions
Factor out the denominator.
-7, 3 and -3 do not work as answers
because they make the denominator zero.
They are called Excluded Values.

8. Simplify
Assume the denominator cannot equal zero.

9. Simplify Assume the denominator cannot equal zero.
Factor out a negative one to move things around

10. Simplify
Assume the denominator cannot equal zero.

11. Simplify
Assume the denominator cannot equal zero.

12. Multiply the fractions
Reduce to simplest form

13. Multiply the fractions
Reduce to simplest form.
Multiply straight across

14. Multiply the fractions
Reduce to simplest form

15. Multiply the fractions
Reduce to simplest form.

16. Multiply the fractions
Reduce before multiply.

17. Multiply the fractions
Reduce before multiply.

18. Multiply the fractions
Reduce before multiply.

19. Multiply the fractions
Reduce before multiply.

20. Multiply the fractions
Reduce before multiply.

21. Multiply the fractions
Reduce before multiply.

22. Multiply the fractions
Reduce before multiply.

23. What is the difference of Division and Multiply of fractions?
Do you remember?

24. What is the difference of Division and Multiply of fractions?
When dividing you multiply by the inverse of the second fraction.

25. Divide the Rational Expressions
You can only Reduce when Multiplying

26. Divide the Rational Expressions
You can only Reduce when Multiplying

27. Definition of Complex fraction
A fraction with fractions in the numerator or denominator.

28. How to simplify a Complex fraction
Remember fractions are division statements.

29. Simplify the Complex fraction
Remember fractions are division statements.

30. Simplify the Complex fraction
Remember fractions are division statements.

31. Simplify the Complex fraction

32. Simplify the Complex fraction

33. Simplify the Complex fraction

35. Homework
Page 476 – 477
# 15,19, 23,
27, 31, 35,
37, 41

36. Homework
Page 476 – 477
# 16,20, 24,
28, 32, 36,
38, 40