9.2 adding and subtracting rational expressions least common denominator of a polynomial of a...
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9.2 Adding and 9.2 Adding and Subtracting Rational Subtracting Rational
ExpressionsExpressions
Least Common DenominatorLeast Common Denominator
of a polynomialof a polynomial
Adding fractions What do you need to add or subtract
fractions?
A common denominator
Of 5 and 3, it is 5 times 3 = 15
(Since both are prime numbers)
We multiply.
Since both numbers divide into
15, it is the Least Common Multiply
3
2
5
1
15
13
15
10
15
3
15
10
5
5
3
215
3
3
3
5
1
What is the L.C.M.
Given the terms
To find the LCM of the numbers, find there factor multiplication.
632532 20,16,15 caandcbbca
52220
222216
5315
What is the L.C.M.
The LCM is the highest number of each factor listed from each number.
632532 20,16,15 caandcbbca
52220
222216
5315
240
222253
LCM
LCM
What is the L.C.M.
The LCM is the highest number of each variable listed from each term.
632532 20,16,15 caandcbbca
63
25
32
20
16
15
ca
cb
bca653240 cbaLCM
Find the LCM of two polynomial
Factor out the polynomial
44
2
2
23
xx
xxx
Find the LCM of two polynomial
Factor out the polynomial
2244
12
22
2
223
xxxx
xxx
xxxxxx
Find the LCM of two polynomial
Factor out the polynomial
2244
12
22
2
223
xxxx
xxx
xxxxxx
221
212
xxxLCM
xxxxLCM
Add the Rational Expressions
Simplify
What is the LCM of 6 and 14
22
2
14
9
6
5
bab
a
42732
7214
326
LCM
Add the Rational Expressions
Simplify
Common denominator 42a2b2
What does 6b times = 42a2b2
What does 14a2b2 times = 42a2b2
22
2
14
9
6
5
bab
a
Add the Rational Expressions
Simplify
Common denominator 42a2b2
What does 6b times = 42a2b2
What does 14a2b2 times = 42a2b2
22
2
14
9
6
5
bab
a
Add the Rational Expressions
Simplify
22
2
14
9
6
5
bab
a
22
2
22
14
9
7
7
6
5
ba
ba
ba
b
a
Add the Rational Expressions
Simplify
22
2
14
9
6
5
bab
a
3
3
14
9
42
35
7
7
6
5
22
22
4
2
22
ba
ba
ba
ba
ba
b
a
Add the Rational Expressions
Simplify
22
2
14
9
6
5
bab
a
2222
4
2222
22
4
2
22
42
27
42
35
42
27
3
3
14
9
42
35
7
7
6
5
baba
ba
baba
ba
ba
ba
ba
b
a
Add the Rational Expressions
Simplify
22
2
14
9
6
5
bab
a
22
4
2222
4
2222
22
4
2
22
42
2735
42
27
42
35
42
27
3
3
14
9
42
35
7
7
6
5
ba
ba
baba
ba
baba
ba
ba
ba
ba
b
a
What are the differences between Adding and Multiplying fractions
Simplify
306
153
153
10
x
x
x
x
What are the differences between Adding and Multiplying fractions
Simplify
56
53
53
10
306
153
153
10
x
x
x
x
x
x
x
x
What are the differences between Adding and Multiplying fractions
Simplify
56
53
532
102
56
53
53
10
306
153
153
10
x
x
x
x
x
x
x
x
x
x
x
x
What are the differences between Adding and Multiplying fractions
Simplify
56
53102
56
53
532
102
56
53
53
10
306
153
153
10
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
What are the differences between Adding and Multiplying fractions
Simplify
56
153202
56
53102
56
53
532
102
56
53
53
10
306
153
153
10
x
xx
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
What are the differences between Adding and Multiplying fractions
Simplify
56
5
56
153202
56
53102
56
53
532
102
56
53
53
10
306
153
153
10
x
x
x
xx
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
The complex fraction
Simplify
11
11
b
ba
The complex fraction
Simplify
11
11
b
ba
1
111
bba
The complex fraction
Simplify
11
11
b
ba
b
b
bab
a
ab
b
bba
1
1111
The complex fraction
Simplify
11
11
b
ba
b
b
ab
ba
b
b
bab
a
ab
b
bba
1
1
1111
The complex fraction
Simplify
11
11
b
ba
b
b
ab
ba
b
b
ab
ba
b
b
bab
a
ab
b
bba
1
1
1
1111
The complex fraction
Simplify
11
11
b
ba
ba
ba
ba
ba
b
b
ab
ba
b
b
ab
ba
b
b
bab
a
ab
b
bba
11
1
1
1
1
1111
Homework Homework
Page 482 – 483Page 482 – 483
## 15, 19, 25, 29, 15, 19, 25, 29,
33, 37, 4133, 37, 41
Homework
Page 482 – 483
# 16, 20, 24, 26,
28, 30, 34, 36
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