 # How do we simplify complex fractions and complex rational expressions?

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

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

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.

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

Example

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

Example

Example

One more for you

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

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

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