How do we simplify complex fractions and complex

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

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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

Example

Example

Try on your own

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