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11-4 Dividing Rational
Expressions
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
The rules for dividing rational expressions are the same as
the rules for dividing fractions.
a c a d
  
b d b c
2x 4x 2x 3x2
 2

5x 3x
5x 4x
6x3

20x2
Rewrite
3x
division as

You
must
10
multiplication
write the
!
answer in
lowest terms
(simplify)!
a c a d
  
b d b c
1
2
1
2x 4x 2x 3x



5x 3x2 5x 4x

3x
10
You can NOT cross
cancel division. However,
when you rewrite the
problem as multiplication
then you CAN cross
cancel.
2
Simplify.
5x2  20x
5x2  20x
1
 x  4 

x

5
x4
x5
Rewrite as multiplication.
1
5xx  4  1
Factor out a GCF.


x5
x4
Cross cancel, if possible.
5x

Multiply numerators
x5
Multiply denominators.
Simplify.
x 3
x 2
x  3 x2  4 x  3
 2
 2

2
x 2
x  4 x  4x  3
x 4
Rewrite as multiplication.
Factor.
Cross cancel, if possible.
Multiply numerators
Multiply denominators.
1

1
x 3
x 2

x  2x  2 x  3x  1
1

x  2x  1
Simplify.
Example 1
Example 2
n 2 n 2

2n n  5
2x  1
1

2x2  x  3 2x  3
Example 3
y 5
2
3y  3y

y2  6y  5
2y2
Example 1 Simplify.
1
n 2 n 2 n 2 n 5



2n n  2
2n n  5
n5

2n
Example 2 Simplify.
2x  1
1
2x  1
2x  3

 2

2
1
2x  x  3 2x  3 2x  x  3
1
2x  3
2x  1


2x  3x  1
1

2x  1
x 1
Remember you
can cancel
factors but not
terms.
Example 3 Simplify.
y 5
3y2  3y

2
y 5
2y2
y  6y  5 
 2
2
3y  3y y  6y  5
2y2
1
1
y 5
2y/2


3/
yy  1 y  5y  1

2y
3y  12
White board
practice –
AGAIN!
Simplify.
4x2 5x 4x2 14
1)



7
14
7 5x
56x2

35x
8x

5
Simplify.
x  3 x2  9 x  3 x  3

 2
2)

x 3 x 3 x 3 x 9
1
1
x 3
x 3


x  3 x  3x  3
1

x 3
Simplify.
x 2 x x 2 6

3)
 
3x  6 6 3x  6 x
1
2

x 2 6

3x  2 x

2
x
Simplify.
4)
x4
1
x4


 3x  3
2
2
x  5x  4 3x  3 x  5x  4
1
1
x4
3x  1


1
x  4 x  1
3
Simplify.
5)
y2  3y  28
16  y2
y2  3y  28 10x  5
1  2x



2
10x  5
1  2x
16  y
-1
-1
y  7 y  4  52x  1

4  y 4  y   1  2x 
5y  7 

4  y 
5y  7 

y4
Simplify.
x  5 4x  6
x 5
8x  40



6)
2x  12 8x  40
2x  12 4x  6
1
1
x  5 4x  6


2x  6 8x  5 
1

4
2
Simplify.
x2  7 x  10
1
x2  7 x  10

 8x  16  2
7) 2
x  2x  35 8x  16
x  2x  35
1
1
x  5x  2
1


x  7 x  5 8x  2
1

8x  7 
Simplify.
x2  5x  4 x2  3x  4 x2  5x  4 2x2  6x

 2

8)
2
2
2
x  3x x  3x  4
x  3x
2x  6x
1
1
1

x  4 x  1 2xx  3


xx  3
x  4 x  1

2x  1
x 1
Simplify.
2
2
x2  6x  8 x2  3x  2  x  6x  8  2x  x  1
9)
 2
2
2
2
2x  9x  4 2x  x  1 2x  9x  4 x  3x  2
1

1
1
x  4x  2  x  12x  1
2x  1x  4 x  2x  1
x 2

x 2
11-A4 Page 597-599 # 10–23,41,50-54.