Multiplication of Rational Expressions

1. Unlocking Skills:
Find the product of the following:
(- 5)(3)
(6)(2)
(-8)(9)
(7)(- 6)
(x)(x)
(-2x)(3x2)
4a(2a-5)
(x+3)(x+4)

2. Unlocking Skills:
Factor the following completely:
2x + 4
X2 - 81
b2 – 18b + 81
1 – y3
c2 +c - 20

3. Find the product of

4. Multiplying Rational Expressions
The objective is to be able to
multiply rational expressions.
a
b
c
d
 8
3
9
16
7
2
4
10
x
x
x
x



5. Observe:
Your Example
Conclusion

6. Grade 8

7. Step 1
Multiply the numerators.
4
3
9
16
2
5
x
x

Multiply the following rational expressions.
4
3
9
16
2
5
x
x

36
3 16
2
5
x
x
METHOD 1

8. Step 2
Multiply the denominators
36
3 16
2
5
x
x
36x2
48 x5

9. Step 3
36
48
2
5
x
x
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.

10. Simplify
36
48
2
5
x
x
3 12
4 12
2
2 3
 
  
x
x x
12
12
3
4
2
2 3
 
x
x x
1 1
3
4
3
43 3
  =
x x

11. 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
x y
2 2
16
4



12. Example
x y
x y
2 2
16
4


Factor each term.
Divide out the common factors
4
4 4




x y
x y
x y
(x-y)(x+y)
(4)(4)
4
(x+y)
(x+y)
(x+y)
(x-y)
4

13. 1 1  =

4
x y
4
x y
Example Continued
4
4 4




x y
x y
x y
Simplify

14. 1.
14
3
12
35
3
2
a
a

2.
9
5
20
27
2
3
5
2 4
rs
v
v
r s

3
8 4
4
7 12
2 1
2
.
x
x
x x
x



 


15. Go…go…go…