Joyce DuVall

1
Multiplying Rational Expressions

• Joyce DuVall
• Green Valley High School
• Henderson, Nevada

2
Multiplying Rational Expressions

• The objective is to be able to multiply rational
  expressions.

3
Step 1
Multiply the following rational expressions.

• Multiply the numerators.

2
36
x
5

3
16
x
4
Step 2
Multiply the denominators
5
Step 3
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.
6
Simplify
2


3
12
x
2
3



4
12
x
x
2
12
3
x


2
3
12
4
x
x
3
3



1
1
3
3
4
4
x
x
7
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.
8
Example
Factor each term.
Divide out the common factors
9
Example Continued



1
1
Simplify
10
You Try It
11
Problem 1
2




2
7
3
4
a
a

Factor each expression
2


3
5
7
a
Divide out common factors
2


3
7
2
4
a
a



2
3
7
5
a
8
8
a
a




1
1
1
Simplify and multiply
5
5
12
Problem 2
Factor each expression

Divide out common factors





Simplify and multiply






1
1
1
1
1
13
Problem 3

Factor each expression
Divide out common factors




Simplify and multiply

1
1