6.4 Complex Fractions
Complex Fractions


A complex fraction is a fraction that has a fraction in
its numerator or its denominator or both.
Examples:
5m
n ,
30mp
3
n
3
5
t
, and
4t
2 2

x y
2 2

x y
Simplifying Complex Fractions

Method 1: Simplify the fraction by doing the
operation indicated, then simplify.

Method 2: Eliminate the smaller fractions by
multiplying both numerator and denominator
by the LCD of the entire fraction.
Example 1 – Method 1
5m
n
30mp
3
n

3
5m
n

n 30mp

2
n
6p
Division was the initial operation indicated.
To perform this division, remember to
multiply the numerator by the reciprocal of
the denominator and then reduce.
Example 1 – Method 2
5m
n

30mp
3
n
3
n
3
n

2
2
5mn
n

30mp 6 p
The LCD for the entire fraction is n3 because we
are looking at n and n3. After you multiply both
numerator and denominator by this LCD, just
reduce.
Example 2 – Method 1
3
3 5t
3  5t
5

t
t
 t t 
4t
4t
4t
3  5t
1
3  5t



t
4t
t 4  t 
Do the
operation
indicated and
subtract the
two terms in
the numerator.
Then rewrite
the division as
a multiplication
problem and
simplify.
Example 2 – Method 2
3
5
t
t

4t
t
3  5t

4  t t
Multiply both numerator and
denominator by LCD of the entire
fraction ( t ) and then simplify.
Example 3 – Method 1
2 2
2 y 2x
2 y  2x


x y
xy xy
xy


2 2
2 y 2x
2 y  2x


x y
xy xy
xy
2 y  2x
xy
2 y  2x



xy
2 y  2x
2 y  2x
2 y  x
yx


2 y  x
yx
Explanation of
Example 3 – Method 1



Do the addition and subtraction indicated in
the numerator and denominator.
Then rewrite the division in the form of
multiplication.
Factor and reduce if possible.
Example 3 – Method 2
2 2

xy
2 y  2x
x y


2 2
xy
2
y

2
x

x y
2 y  x
yx


2 y  x
yx
Explanation of
Example 3 – Method 2


Multiply both numerator and denominator by
LCD of entire fraction.
Then factor and simplify if possible.
Other instructions



Unless specified, you may use either Method
1 or 2, whichever one you prefer.
Please look at all of the examples in the
book.
Please do assignment 6D for homework.