Seconda ry Ill
Unit 3.3 Notes: Adding and Subtracting Rational Expressions
Review:
(_,-~)
3
0 _l__
_r_+
(X'-+z) LL 0
(x-~0+2) (!-3)7Jcn)
- "3
~><
X~
rr\
St eps to
c;
1:..
i-
"X
0
(x -3)('><:-t'l}
[:;]
: Lx -t?..) ~-'3)
E
:f -2. J
-+~
(x~~)l;<+ 2)
'2-"X- \
~ubtract rational expressions:
Lx-3)(x+2)
1. To add or subtract fracti ons you need to find a common enominator. t_(.,
D
**To Find a common denominator: Factor all denominat ors (where possible} first **
2.
Give restrictions.
3. Multiply the numerator and denominator of each term by the missing parts of the common
denominator
4. Keep the common denominator and add or subtract term s in the numerator.
5. Simplify f ina l answe r where possible.
Example 1: Calculate the least common denominator for each pair of rational expressions
3
7x
. (x+4)' ~-4)
a--
-2
LCD:
4x
b. 3x- 2' x 2 +7x-6
- 11
C.
7
7' x-4
X
1
x 2 - 16
LCD:
J
('';,X-z.)( X 2. ~ 7 X - ~
LCD : X
l
X
- Lf)
(x-+Lf)
(><-'fY-)(-44)
z.x
d.
7 x+ll
x 2 -5x+6 ' x 2 -6x+9
LCD:
L )( - 2.) ( )( - 1) L><-:3)
i)
Secondary Ill
Example 2: Add or subtract the following rational expressions. List restrictions.
U D: \"2.
--s
'}(
,
\
-·(
.
(
\ . r;d
:;
'
'1~/
'I
2 ~~-2y)+ ~ - ~ (~'
if
3
12
4
-3.)
-P
&:ey -r ~ - _y:f>
-3fo~~
~jW '(~-=~~
L__- - ' ~
-~
'1
1'2
Sx
-IDx -
Sx
'L'1
Sx
-Sx3 -2'1 x2- -t '5x + 2.-\
3 (Zx +3)
2
-