Download How do we simplify complex fractions and complex rational

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.
5
6
2
3
1
2
2
5
4
1
1
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.
5
6
2
3
5 2
 
6 3
5 3
 
6 2
5

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
Example
1
2
2
5
Try on your own…
4
1
1
3
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
1
x
x
x 1

1
 (x  )  (x  1)
x
x 2 1
1
(
)
x
x 1
x 1
(x 1)(x 1)
1

, x  0,1


x
x
x 1



Example
x2
5 6
1  2
x x
Try on your own
2
3x
1
x
One more for you
16
x
x
x 2  8x  16
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