Joyce DuVall
Green Valley High School
Henderson, Nevada
Multiplying Rational Expressions
The objective is to be able to
multiply rational expressions.
a c

b d
8 x 9 x

2
10
3x 16 x
7
4
Step 1
Multiply the following rational expressions.
2
4x
9

3 16x 5
Multiply the numerators.
2
4x
9

5
3 16x
2
36x
5

3 16x
Step 2
Multiply the denominators
36 x
2
3  16 x
2
5
36x
5
48x
Step 3
2
36x
5
48x
Simplify the resulting
expression by dividing out the
greatest common factor of the
numerator and denominator.
The greatest common factor (GCF) of 36
and 48 is 12.
The greatest common factor (GCF) of
x2 and x5 is x2.
Simplify
2
2


3 12 x
36x
5
48x
2  3


4 12 x x
2
12 x
3
 2 3
12 x
4x
3
3
1 1 3 = 3
4x
4x
Method 2
When the rational expressions become
more complex or the numbers become
larger, it is sometimes easier to divide
out the common factors and then
multiply. This is the case for the
following example.
x y
4

16
xy
2
2
Example
x y
4

16
xy
2
Factor each term.
Divide out the
common factors
2
( x  y )( x  y )
4

44
xy
4 xy xy


4 xy
4
Example Continued
4 xy xy


4 xy
4
Simplify
xy xy
=
1 1
4
4
1.
14 a 3 12

2
3
35a
2
A
5
2.
9 rs
20v

3
2 4
5v
27 r s
A
3.
8x  4 x  7 x  12

x4
2x  1
A
2