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Adding/Adding/Subtracting Subtracting
Rational Rational ExpressionsExpressions
Mr. Peter RichardWill be instructionalizing you on:
Adding and Subtracting Rational Adding and Subtracting Rational Expressions with the Same Expressions with the Same
DenominatorDenominator
In the Nut Shell
To add or subtract rational expressions with the same denominator, just add or
subtract the numerators and keep the same denominator.
* No grouping symbol for the final answer.
EXAMPLE 1• Add. Write each answer in lowest
terms.
Solution:
Adding Rational Expressions with the Same Denominator
Slide 7.4 - 4
7 3
15 15
2 2x y
x y x y
7 3
15
10
15
5
2
3
5
2
3
2 2x y
x y
2 x y
x y
2
Example 2: 2222
5374
yx
y
yx
y
22
)53(74
yx
yy
22 yx
12y
Example 3:
5
419
5
952 22
x
xx
x
xx
5x
49x19x5xx2 22
5x
5x14x3 2
5x
5x1x3
))((
3x+1
Factor the Numerator!
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
Quiz Time!!Quiz Time!!
• See Worksheets for Quiz and Homework!
Adding and Subtracting Rational Expressions with Different Denominators
In the Nut Shell
To add or subtract rational expressions with different denominators, first find the LCD (the least common multiple
of the denominators). To find the LCD of two
or more algebraic expressions, first factor each expression. Then use each factor the greatest number of times it
occurs in any factorizations.
* No grouping symbol for the final answer.
Example 3: a12
b5
8
a7
1x
3
1x
x5
x2
12
Example 4:
Example 5:
6y5y
3y
6y7y
1y222
