In multiplying rational expressions, we use the following rule:

1
Multiplying and Dividing Rational Expressions.
In multiplying rational expressions, we use the
following rule
Dividing by a rational expression is the same as
multiplying by its reciprocal.
2
To multiply rational expressions we use the
following steps

1. Multiply the numerator and multiply the
   denominator.

1. Factor completely the numerator and the
   denominator.

3. Cancel common factors and simplify
3
Multiply
Factor 16 and use product rule to multiply.
Cancel common factors and simplify
4
Multiply
Factor numbers on numerator and denominator.
Cancel common factors and use quotient rule.
5
Multiply
6
Multiply
Factor numerator
Cancel common factors and use quotient rule
3(a b)
7
Divide
Dividing by a rational expression is the same as
multiplying by its reciprocal.
Change the division to a multiplication and
invert the divisor.
Factor numbers and use product rule
8
Cancel common factors
Use quotient rule
9
Divide
Change the division to a multiplication and
invert the divisor.
Use quotient rule
10
Divide
Change the division to a multiplication and
invert the divisor.
Factor each expression
11
x
x
9
-2
x2 7x 18
(x 9)(x 2)
x
x
x2 17x 30
(x 15)(x 2)
3x 3 3(x 1)
-15
-2
Cancel common factors
12
Divide
Change the division to a multiplication and
invert the divisor.
Factor common factors.
Factor all expressions
Cancel common factors
13
Divide
Change the division to a multiplication and
invert the divisor.
Factor all expressions.
x
x
x2 y2 (x y) (x y)
- y
- y
x2 2xy y2
(x y) (x y)
(x y)2
14
Cancel common factors
15
2x
x
Multiply
Factor common factors.
- 1
- 3
Factor all expressions
x
x
2x2 7x 3
(2x 1) (x 3)
- 1
3
x2 2x 3
(x 3) (x 1)
16
Cancel common factors
17
r
Divide
3r
Change division to multiplication.
2s
5s
Factor all expressions
3r
2r
- s
5s
3r
2r
Cancel common factors
-s
-s
3r
2r
2s
-s
18
Divide
Change the division to a multiplication.
Factor all expressions.
r
r
r2 r 6 (r 3) (r 2)
- 2
6
r2 4r 12
(r 6) (r 2)
Cancel common factors