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ADDING AND SUBTRACTING RATIONAL EXPRESSIONS:
TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE
THE ADDITION PROPERTY:
b
ca
b
c
b
a
IF THE EXPRESSIONS HAVE THE SAME (COMMON) DENOMINATOR, ADD OR SUBTRACT THE NUMERATORS, KEEP THE SAME DENOMINATOR, AND SIMPLIFY THE RESULT.
x
a
x
a
x
a
x
a 2
3
6
3
4
3
2
DO THE OPERATIONS AND SIMPLIFY THE RESULT:
4
5
x
x4
5
4
xx
x
4
3
4
2
4
4
x
x
x
x
x
4
4
x
x=1
)4(
)4(
x
x
HERE’S AN EXAMPLE …
1213
3
1213
4222
xx
x
xx
x
1213
)3(422
xx
xx
1213
12
xx
x
)12)(1(
)1(
xx
x
12
1
x
HERE’S ANOTHER …
yx
y
yx
x
99
yx
yx
99
yx
yx
)(9
= 9=
AND ANOTHER …
To add or subtract fractions with different denominators find the least common denominator (LCD), change
each fraction so that it has that denominator then add or subtract
Simply stated, the LCD is the smallest number (expression) that is
evenly divisible by all denominators.
xy
xy
yx
2323
xy
y
xyx
2323
AND ANOTHER …
ONE MORE …
)2)(2(
5)2(4)2(3
)2)(2(
5
)2(
4
)2(
3
xx
xx
xxxx
TO FIND THE LCD
•FACTOR EACH DENOMINATOR
•WRITE THE DIFFERENT FACTORS
•GIVE EACH FACTOR THE HIGHEST POWER TO WHICH IT OCCURS
•MULTIPLY THE RESULTS
ADD :
•LCD =
•CHANGE EACH FRACTION TO LCD
•ADD/SUBTRACT
•SIMPLIFY
m
n
n
m
4
3
2
5
mn4
mn
nn
mn
mm
4
)(3
4
)2(5
mn
nm
4
310 22
ADD :
•LCD =
•CHANGE EACH FRACTION TO LCD
•ADD/SUBTRACT
•SIMPLIFY
1
12
x
1x
1
1
1
)1(2
xx
x
1
122
x
x
1
12
x
x
ADD :
•LCD =
•CHANGE EACH FRACTION TO LCD
•ADD/SUBTRACT
•SIMPLIFY
6
4
3
7
x
x
x
63 xx
63
34
63
67
xx
xx
xx
x
)6)(3(
42194
63
124427 22
xx
xx
xx
xxx
(Numerator isn’t factorable)
1)
24
8
2
2
2 yyy
y
2)107
32
152
53
6
12222
xx
x
xx
x
xx
x
3)
9
32
x
x
4) 121
2
1
222
xx
x
x
x
x
YOU TRY!
9
32
x
x
)9(
3)9()9(2
x
xxx
)9(
39182 2
x
xxx
)9(
15112
x
xx
1.
107
32
152
53
6
12222
xx
x
xx
x
xx
x
(x+3) (x-2) (x+3) (x-5) (x-5) (x-2)
)5)(2)(3(
)3)(32())2)(53(()5)(12(
xxx
xxxxxx
)5)(2)(3(
)932()10113()5112( 222
xxx
xxxxxx)5)(2)(3(
)143( 2
xxx
xx
2.
=
=
24
8
2
2
2 yyy
y
(y – 2) (y+2) -(y-2)(y+2)
)2)(2(
)8)(1()2)(2()2(
yy
yyy
)2)(2(
84222
yy
yyy
)2)(2(
42
yy
y1
)2)(2(
)2)(2(
yy
yy
3.
= =
121
2
1
222
xx
x
x
x
x
(x-1) (x-1)(x+1) (x+1)(x+1)
LCM: (x-1)(x+1)(x+1)
)1)(1)(1(
)1()1(2)1)(1(2
xxx
xxxxxx
)1)(1)(1(
22)12(2 222
xxx
xxxxxx
)1)(1)(1(
)23(1
)1)(1)(1(
23 22
xxx
xx
xxx
xx
4.
