6.1 SIMPLIFYING RATIONAL EXPRESSIONS
PC 11
Name___________________________
Date: ______________________
Block: _______
1. Determine the restriction(s) on the following rational expressions.
a.


2(x  5)
e.
3x(2x 1)

b.

x3
x3
x  3
d.
x3
(x  3)( x  4)
g.
(x  3)(x  2)

x 2
x2  2
d.
(x  3)(x  1)
(x  5)(x 1)
h.
x2  y2
x2  y2

x2  4
g. 2
x  5x  6
b.

x 1
1 x
(x  4)(x  2)
e.
4(x  2)

c.
x 1
1 x
f.
(x 1)(x  2)( x  3)
(x  1)(x  2)( x  3)


(x 1)(2  x)(x  3)
h.
(x  2)(x  3)

i.
x 2 1
1 x 2
j.
3(x  5)(x  7)(x  1)
7(5  x)(1 x)(7  x)

3. Reduce to lowest terms. Assume no denominators are zero.
6x 2 y
c.
12x 2 y  9xy 2
5xy
b.
2
5x  10xy
3m
a.
3m  6

c.
x 2  3x  4
f.
x 2  2x


x5
x3



2. Simplify the following rational expressions. Assume no denominators are zero.
a.

5
x


14 x 2 y
d.
21x 2 y  35xy 2

e.

3n  12m
g.
20m  5n
4x  8
2x  4
f.

3a 12
h.
6a  24

x 2  7x  12
l.
x4
9  3x
k. 2
x  3x
x 2 10x  25
m.
5 x

2x 2  6x
i.
5x


2x 2 10x
j.
4 x  20
2x 10
3x 15
x2  x  6
n.
2 x


4. Reduce to lowest terms. Assume no denominators are zero.
a.

18x 2 y
b.
3xy 2
4ab
8ac
25a 3b 2c
d.
40ab 7
8x 2 yz
c.
24 xyz2



5. Simplify. Assume no denominators are zero.
a.
a 2  7a  10
a 2  5a  6
x 2 16
b. 2
x  4 x  32


r 2  7r  12
c. 2
r  3r  4
x 2  8xy  12y 2
d. 2
x  2xy  24 y 2


Answers:
1a. x≠ 0
2a. 1
3a.
b. -1
m
m 2
x
3j. 2
4a.
b. x ≠ 3
b
2c
c. no restrictions.
c. 1
d. -1
y
d. x ≠ -5, 1
e. x ≠ 0, 0.5
f. x ≠ 0, 2
x

4
x 1
x 4
e.
f.
g. ( x  2 )
h. x - 1 i. -1
x 1
4
2x
4 x 3 y
b. x  2 y
c.
3
k.  x
l. x + 3
6x
b.  y
c.
x
3z
d.
2x
3 x 5 y
3m. –x + 5
d. 
5a 2 c
8b 5
e. 2
f.
2
3
g. x ≠ 2, 3
3
j. 7
h. x ≠ -y, y
3
1
g.  5 h.
2
i.
2 x 6
5
n. –x – 3
5a.
a 5
a 3
b.
x 4
x 8
c.
r 3
r 1
d.
x 2 y
x 4 y