Section 2.1 Handout (Complex Fractions Review)
Method 1: Simplify the numerator and
denominator separately, then rewrite as
the division of two fractions. Multiply by
the reciprocal of the 2nd fraction and
simplify.
Method 2: Multiply both numerator
and denominator by the least common
denominator of all the “little” fractions
This will clear both numerator and
denominator of fractions. Simplify.
x 5
2 x 2 15


Method 1: 3 2 x  6 x 6 x
1
1
2
x
x2
Method 2:
x 5

3 2x 
1
x2
x 5 
2
   6x 
3
2
x


 1 
2
 2  6x 
x
 
LCD is 6x 2
2 x 2  15
6x

1
x2
x
5
6 x2    6 x2 

2x
Distribute
3
1
2
6x 
x2
2 x 2  15
1

 2
6x
x
2 x3  15 x

6

2 x 2  15 x 2

6x
1

2 x  15 x  x

6x
1
(cancel the
common factor x):
You can write the answer either way.
2

x  2 x 2  15 
6
Simplify the following complex fractions. Use either method 1 or 2.
4
x
5x
1) 7 3
10 x
7
2)
1 1

a
6) 2 b2
a b
xh2 x2

3
3
7)
h
2
6

x x 1
5
3)
2
3
9
4
8)
2x 
4)
1
2
4
3
3

x  h 1 x 1
h
x5
5) x  x  6
1
x3
2
Answers:
1)
1
2x 2
2)
2x  2
or
2 x  1
3)
68
27
4)
4x 1
8
5)
x5
x2
6)
1
1
or 2
ab(a  b)
a b  ab 2
7)
1
3
2  2x
2x 1
3
8) ( x  1)( x  h  1)