3.10 Add/Subtract Rational Expressions Example 1 Add and subtract with the same denominator Find the...
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3.1 0 Add/Subtract Rational Expressions Example 1 Add and subtract with the same Add and subtract with the same denominator denominator Find the sum or difference. Find the sum or difference. x x a 8 4 8 3 . x 8 3 4 x 8 7 Add numerators. Add numerators. Simplify. Simplify. 1 7 1 9 2 . x x x b x x a 8 4 8 3 .
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Transcript of 3.10 Add/Subtract Rational Expressions Example 1 Add and subtract with the same denominator Find the...
3.10 Add/Subtract Rational Expressions
Example 1 Add and subtract with the same denominatorAdd and subtract with the same denominator
Find the sum or difference.Find the sum or difference.
xxa
8
4
8
3 .
x8
3 4
x8
7
Add numerators.Add numerators.
Simplify.Simplify.
1
7
1
92 .
xx
xb
xxa
8
4
8
3 .
3.10 Add/Subtract Rational Expressions
Example 1 Add and subtract with the same denominatorAdd and subtract with the same denominator
Find the sum or difference.Find the sum or difference.
xxa
8
4
8
3 .
1
x92 x 7
1
x
22 x
Add numerators.Add numerators.
Simplify.Simplify.
1
7
1
92 .
xx
xb
1
7
1
92 .
xx
xb
2 1x
1xFactor and divide out Factor and divide out common factor.common factor.
___ Simplify.Simplify.2
3.10 Add/Subtract Rational Expressions
xx
x
4
3
4
8 .1
Checkpoint. Find the sum or difference. Checkpoint. Find the sum or difference.
x4
x 11
x
x
x
x 5256 .2
x
x4 4
3.10 Add/Subtract Rational Expressions
Example 2 Find the LCD of rational expressionsFind the LCD of rational expressions
Find the LCD of the rational expressions.Find the LCD of the rational expressions.
43 4
5 ,
3
1 .
xxa
2
3 ,
4
7 .
22
xx
x
xb
a. Find the ______________________ of 3x3 and 4x4.least common multiple
_____________3 3 x 3 x x x
_____________4 4 x 4 x x x xWrite prime factorization.Write prime factorization.
Circle common factors.Circle common factors.
__________LCM Factors inside circle.Factors inside circle.xxx Factors outside circle.Factors outside circle.
x 43 ___ 412x
The LCD of and is ______.33
1
x 44
5
x412x
3.10 Add/Subtract Rational Expressions
Example 2 Find the LCD of rational expressionsFind the LCD of rational expressions
Find the LCD of the rational expressions.Find the LCD of the rational expressions.
43 4
5 ,
3
1 .
xxa
2
3 ,
4
7 .
22
xx
x
xb
b. Find the ______________________ of x2 – 4 and x2 + x – 2 least common multiple
_________42 x 2x 2x
_________22 xx 2x 1x
_______________LCM 2x 2 x
The LCD of and is
__________________________.
42 x 22 xx
1 x
2x 2x 1x
3.10 Add/Subtract Rational Expressions
34
2 ,
36
5 .3
x
x
x
Checkpoint. Find the LCD of the rational expression. Checkpoint. Find the LCD of the rational expression.
x36 4 9 x34x 4 x x x
___________LCM x4 xx9 336x
3.10 Add/Subtract Rational Expressions
3
1 ,
8
7 .4
x
x
x
x
Checkpoint. Find the LCD of the rational expression. Checkpoint. Find the LCD of the rational expression.
___________LCM 8x 3x
3.10 Add/Subtract Rational Expressions
Example 3 Add expressions with different denominatorsAdd expressions with different denominators
Find the sum .Find the sum .
Rewrite fractions using Rewrite fractions using LCD, ______.LCD, ______.
43 4
5
3
1
xx
412x 4
5
3
143
xx x4
x4
3
3
Simplify numerators and Simplify numerators and denominators.denominators.
x4
412x
15412x
154 x
412xAdd fractions.Add fractions.
3.10 Add/Subtract Rational Expressions
Example 3 Subtract expressions with different denominatorsSubtract expressions with different denominators
Find the difference .Find the difference .9
4
65
122
x
x
xx
x
________
4
________
1
xx
3x 2x 3x 3x
____________
____4
____________
____1
xx
3x 2x 3x 3x3x
3x2x
2x
3x 2x 3x
2x x3 x 3 2x x2 x4 8
3x 2x 3x
5
3.10 Add/Subtract Rational Expressions
13
15
1
9 .5
xx
Checkpoint. Find the sum or difference. Checkpoint. Find the sum or difference.
____13
____15
____1
____9
xx
13 x13 x
1x1x
131
xxx27 9 x15 15
131
xxx12 24
131
xx 12 x 2
3.10 Add/Subtract Rational Expressions
4
3
5
12 .6
x
x
x
Checkpoint. Find the sum or difference. Checkpoint. Find the sum or difference.
____4
____3
____5
____12
x
x
x
4x4x
x5x5
45
xxx12 48 215x
45
xxx12 48
45
xx 3 25x x4215x 16
3.10 Add/Subtract Rational Expressions
65
4
242
1 .7
22
xxxx
xCheckpoint. Find the sum or difference. Checkpoint. Find the sum or difference.
____________
____4
____________
____1
x 1x1x
4x4x
146
xxx
2x x x
6x 4x 6x 1x
1 x4 16
146
xxx
2x x4 15
3.10 Add/Subtract Rational Expressions
214
6
152
2 .8
22
xx
x
xx
xCheckpoint. Find the sum or difference. Checkpoint. Find the sum or difference.
____________
____6
____________
____2
xx 7x7x
5x5x
735
xxx
2x x7 x2
5x 3x 7x 3x
14 2x x5
x6 30
735
xxx44x10
735
xxx 2 x5 22
3.10 Add/Subtract Rational Expressions
Pg. 189, 3.10 #1-21
