Adding and subtracting rational expressions:
description
Transcript of Adding and subtracting rational expressions:
Adding and subtracting rational expressions:
To add or subtract rational expressions use the addition property:
b
ca
b
c
b
a
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
Do the operations and simplify the result:
4
5
4
xx
x
4
5
x
x
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
4
3
4
2
4
4
x
x
x
x
x
4
4
x
x
=1)4(
)4(
x
x
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
yx
y
yx
x
99
yx
yx
99
yx
yx
)(9
=9Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
xy
xy
yx
2323
xy
y
xyx
2323
)2)(2(
5)2(4)2(3
)2)(2(
5
)2(
4
)2(
3
xx
xx
xxxx
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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 least number (expression) that all denominators
will divide into evenly.
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
To find the LCD
• factor each denominator• write the different factors• give each factor the highest power
to which it occurs• multiply the results
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
Find the LCD for y²-16 and y²-8y+16
• Factor each• write each factor• give each highest exponent• multiply results
• (y+4)(y-4) and (y-4)²
• (y+4)(y-4)
• (y+4)(y-4)²• (y+4)(y-4)²
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
Add : m
n
n
m
4
3
2
5
• LCD =• change each
fraction to LCD
• add/subtract• simplify
mn4
mn
nn
mn
mm
4
)(3
4
)2(5
mn
nm
4
310 22
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
(Top isn’t factorable)
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
If the denominators have opposite factors, then change one
of them using the 3 signs of a fraction rule.
b
a
b
a
b
a
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
2
42
x
x
2
1
2
3
x
x
x
x
2
1
)2(
)3(
x
x
x
x
2
1
2
3
x
x
x
x
2)2(
)2(2
x
x
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
9
32
x
x
)9(
3)9()9(2
x
xxx
)9(
39182 2
x
xxx
)9(
15112
x
xx
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
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
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
Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
xy
yx
3
3
Simplify the top and bottom:
yxyxxy
3
3
x
y
xxy
yxy
)3(
)3(Use “tortilla method”