DATE
PERIOD
Study Guide and Intervention
Si m plifyi ng Rati on al Expressions
Identify Excluded Values
Bational
Expression
an algebraic fraction with numerator and
denominator that are polynomials
Example:
ft1
Because a rational expression involves division, the denominator cannot equal zero. Any
value of the denorninator that results in division by zero is called an exeluded value of
the denominator.
State the excluded
State the excluded
a Ofa 4m-8
\/alUe
values
Exclude the values for which m + 2 : 0.
m * -.2 = 0
The denominator cannot equal 0.
m + 2 - 2 - 0 - 2 Subtract2from eachside.
Exclude the values for which x2
m+2
1
of ':+
x"-9
x2
.
- I : 0
(r+3Xr-S):0
x * 3 = 0 or x -
m: -2
Simptify.
Therefore, m cannot equal -2.
--d
Therefore,
I
- I:
O.
The denominator cannot equal 0.
Factor.
3
: 0
Zero Product Property
_e
-u
r cannot equal -3
or
3.
Exercises
State the excluded values for each rational expression.
C
li
,g
6
q
c
o
o
=
I
L#r
x2-2
n -._
rr.
x'+
4
q 72-a
2.-
4.
B
o
o
o
D.
F
2n.
-
12
n2-4
6.
32+ct
m2-4
2rn')
-
8
2x+78
x2*L6
o
c
x2-4
8.
h2-2k+l
10.
.9
,I
E
7.
j
=
o
9.
o
o
c
I
o
o
h.2+4k+3
a-l
a2+5a+6
m2-L
2m2-mZx'+
11.
25-nz
n2-4n-5
12.
13.
n2-2n-3
n2+4n-5
14.
y'-y-2
3y2 - 12
15.
h2+2h-B
k2-20k+64
16.
x2+4x+4
4x2+l1;x-3
o
,o
x\4x+4
Chapter
'l
1
17
bx +
12-10*+16
Glencoe Algebra
1
NAME
I
DATE
I.I
Study Guide and lntervention
Si mplifying Rational Expressions
-
kontinued)
Simplify Expressioos Factoring polynomials is a useful tool for simplifying rational
expressions. To simpiify a rational expression, first factor the numerator and denominator.
Then divide each by the greatest common factor.
simplify
5423
(62)(922)
24yz
-: :-
W
The GCF of the numerator and the denominator is 62.
{62)tay)
*u)(9zz)
Divide the numeraior and denominator by 62.
k*z)(4y)
Q.2
=-4y
Simplify.
3'- 9
Sirnolifv
' " x' -5r+6 . State the excluded
3(x - 3)
Factor.
(x-2)(x -3)
3r-9
[email protected]
- 2)k-ST,
(x
Divide by the GCF, x
,
*-2
d
Exclude
(x
values for which x2
x"-ax 6=0
- 2)(x 3):0
X:2
values of
r.
- 3.
Simplify.
-
5x
*
6
:
0.
o
o
!
^-_o
5.
I-J
Therefore,
@
f
{2andrc+3.
@
o
o
o
o
Simplify
D
expression. State the excluded values of the variables.
=
_-
,
q
IZab
a'b'
b.
11.
I.3.
xt-4
2n.-8
n2-LG
x2x2+4x
k2_
k2+4k
n2n2-4n
n'+ ln
n2+2n
Ghapter
11
7n't
9.
=:
o
2lnn
- r*2
11.-
;o
,
m'-4
m'+6m+8
^ x2+2x+l
b.-
4
J
4.-
o
o
p
{
x'-7
=
o
a2+3a+2
a2+5a+6
m2-2m+l
10.
2m2-m-1
x2+x-6
12.
o
:
8.
5
t2
s
o
I=.
J
2x2-B
L4.
18
.,1
JJ
",
')
y')- t}y + 16
Glencoe Algebra
1