adding and subtracting rational expressions: to add or subtract rational expressions use the...
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![Page 1: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/1.jpg)
ADDING AND SUBTRACTING RATIONAL EXPRESSIONS:
TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE
THE ADDITION PROPERTY:
b
ca
b
c
b
a
![Page 2: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/2.jpg)
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
![Page 3: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/3.jpg)
DO THE OPERATIONS AND SIMPLIFY THE RESULT:
4
5
x
x4
5
4
xx
x
![Page 4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/4.jpg)
4
3
4
2
4
4
x
x
x
x
x
4
4
x
x=1
)4(
)4(
x
x
HERE’S AN EXAMPLE …
![Page 5: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/5.jpg)
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 …
![Page 6: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/6.jpg)
yx
y
yx
x
99
yx
yx
99
yx
yx
)(9
= 9=
AND ANOTHER …
![Page 7: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/7.jpg)
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.
![Page 8: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/8.jpg)
xy
xy
yx
2323
xy
y
xyx
2323
AND ANOTHER …
![Page 9: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/9.jpg)
ONE MORE …
)2)(2(
5)2(4)2(3
)2)(2(
5
)2(
4
)2(
3
xx
xx
xxxx
![Page 10: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/10.jpg)
TO FIND THE LCD
•FACTOR EACH DENOMINATOR
•WRITE THE DIFFERENT FACTORS
•GIVE EACH FACTOR THE HIGHEST POWER TO WHICH IT OCCURS
•MULTIPLY THE RESULTS
![Page 11: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/11.jpg)
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
![Page 12: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/12.jpg)
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
![Page 13: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/13.jpg)
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)
![Page 14: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/14.jpg)
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!
![Page 15: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/15.jpg)
9
32
x
x
)9(
3)9()9(2
x
xxx
)9(
39182 2
x
xxx
)9(
15112
x
xx
1.
![Page 16: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/16.jpg)
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.
=
=
![Page 17: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/17.jpg)
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.
= =
![Page 18: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS: TO ADD OR SUBTRACT RATIONAL EXPRESSIONS USE THE ADDITION PROPERTY:](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f395503460f94c55dd4/html5/thumbnails/18.jpg)
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.