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L E S S O N Simplifying Complex Fractions 92
Warm Up
1. Vocabulary For any nonzero real number n, the of the number ( ( 1 1 1 1 ) ) i s _1 .
n
Identify the LCM.
2. 4x - 16 and x - 4
(57) Factor.
4.x2 -4x-77 (72)
3. 18x2 and 9x (57)
5.18x2 +12x+2 (83)
NewConcepts Acomplexfractionisafractionthatcontainsoneormorefractionsinthe numerator or the denominator.
A complex fraction can be written as a fraction divided by a fraction. The rules for dividing fractions can be applied to simplify complex fractions.
Simplifying by Dividing
__a Simplify _x .
SOLUTION
x __a
Complex Fractions
There are two ways to write a fraction divided by a fraction. _a
_b =_a ÷_c,whenb≠0,c≠0,andd≠0. _c b d
d
Example
1
b a+x
Math Reasoning
Write Explain why the
c_omplex fraction
_a x
_
written as x ÷ a + x .
can be a + x _a
b
_
b
b a+x
= _a ÷ _b
x a+x
Write using a division symbol. Multiply by the reciprocal.
Multiply.
= a · a + x __
_x
= a(a + x)
xb
b
Lesson 92 609
