1. How do we simplify complex fractions and complex rational expressions?
Do Now
Finish this sentence:
Dividing by a fraction is the same as…

2. What is a complex fraction?
A complex fraction is fraction with another fraction in the numerator or denominator.
Ex.

3. So how can we simplify them?
Remember, fractions are just division problems.
We can rewrite the complex fraction as a division problem with two fractions.
This division problem then changes to multiplication by the reciprocal.

4. What if we have mixed numbers in the complex fraction?
If we have mixed numbers, we treat it as an addition problem with unlike denominators.
We want to be working with two fractions, so make sure the numerator is one fraction, and the denominator is one fraction
Now we can rewrite the complex fraction as a division of two fractions

5. Example

6. Try on your own…

7. What about complex rational expression?
Treat the complex rational expression as a division problem
Add any rational expressions to form rational expressions in the numerator and denominator
Factor
Simplify
“Bad” values

8. Example

9. Example

10. Try on your own

11. One more for you

12. Review Treat the complex fraction as a division problem
Change any mixed numbers into improper fractions
Simplify
“Bad” values

13. Summary/HW
What are some challenges or potential pitfalls that one must remember when dealing with complex fractions?
HW pg 128, 1-19 odd