Download 6.8 Multiplying and Dividing Rational Expressions

6.8 Multiplying
and Dividing
Rational
Expressions
multiplying
rational
expressions, we use the same rules as we
do for multiplying rational numbers.
 When
 Theorem:
For all r, s, t, and u, t and u ≠ 0,
r s rs
 
t u tu


divide
When we
rational expressions we
multiply
reciprocal
can
by the
and then use the first theorem on multiplication.
Theorem:
For all r, s, t, and, u, and s, t, and u ≠ 0
r s r u ru
   
t u t s ts

For either case, we can then
cancel
expression and
factor
all
common factors.
Simplify
1.
p  4 p  5 p  3p

3
p
2 p  10
2
2
Simplify
2.
5
c  3c  10

2
c  5c
5c  10
2
Simplify
3.
v  6v  9
v 9
 2
3
v  25v
v  3v  10
2
2
Simplify
4.
a a  b  a 3  2a 2b  ab 2

3
3
a b
a 2  ab  b 2
3
3
 Sometimes
you may need to find a
denominator and
common
combine two expressions before simplifying.
Simplify
5.
g
g 
 h  h   h  1
2
2
Simplify
6.

x

4 x  x 
1
1

2