Download Reteach 8-3 - Humble ISD

Name
Date
Class
Reteach
LESSON
8-3
Adding and Subtracting Rational Expressions
Use a common denominator to add or subtract rational expressions.
8
______
4 2x
______
.
Add: 6x
x5
x5
Step 1 Add.
8 6x
4 2x 8
6x
4 2x
______
______
______________
x5
x5
x5
6x
2x
48
______________
x5
4
______
8x
x5
The denominators are the same.
Add the numerators.
Group like terms.
Combine like terms.
Step 2 Identify x-values for which the expression is undefined.
x 5 because 5 makes the denominator equal 0.
2
______
3 8x
______
.
Subtract: 4x
2x
1
2x 1
Step 1 Subtract.
The denominators are the same.
4x 3 8x 2 2 _________________
4x
3 8x
______
______
Subtract the numerators.
2x 1
2x 1
2x 1
3 8x 2
______________
4x
Use the Distributive Property.
2x 1
5
________
4x
Combine like terms.
2x 1
Step 2 Identify x-values for which the expression is undefined.
1 makes the denominator equal 0.
1 because __
x __
2
2
Add or subtract.
2
______
x 5 3x
1. ______
2
2
x 4
x 4
1
______
5 4x
______
2. 7x
x3
x3
________________
x 5 3x 2 x2 4
x
4x
3
______
2
x 4
2, 2
9x
1 ______
______
4. 4x
3x 7
3x 7
x
_________________
7x 5 4x 1 x3
x
3x
4
______
x3
3
5x
8 x _____
5. _____
x3
x3
3x
10
_______
3x 7
7
__
3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c08-3_rt.indd 22
4
______
1 5x
______
3. 2x
x1
x1
2x
1 5x 4 _________________
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5
________
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1
x
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5x 2
______
6. ______
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x2 1
2x
9
______
2
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3
_____
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3
x
22
x
1
Holt Algebra 2
12/26/05 6:56:33 AM
Process Black
Name
LESSON
8-3
Date
Class
Reteach
Adding and Subtracting Rational Expressions (continued)
Use the least common denominator (LCD) to add rational expressions with different
denominators. The process is the same as adding fractions with different denominators.
2x
x4
_____ .
Add: __________
2
x
1
x 2x 3
Step 1 Factor denominators completely.
x4
2x
x4
2x _____________
__________
_____
_____
x 3 x 1 x1
x1
x 2 2x 3
Step 2 Find the LCD.
The LCD is the least common multiple of the denominators:
x 3 x 1 .
Step 3 Write each term of the expression using the LCD.
3 _____________
2x 6x
2x x_____
2x _____
_____
x 1 x 3 x1
x1 x3
2
2x 6x
x4
2x _____________
x4
So, _____________
_____
_____________
x 1 x 3 x 3 x 1 x 3 x 1 x1
2
Step 4 Add the numerators and simplify.
2
x_______________
4 2x 6x _____________
2x 2 7x 4
x 3 x 1 x 3 x 1 Step 5 Identify x-values for which the expression is undefined.
x 3 or 1 because both values make the denominator equal 0.
Add.
3x
x 1 _____
7. ______
2
x
2
x 4
3
4x 1
_____
8. __________
2
x
1
x 3x 2
3x
x1
2
_____________
_____ x_____
x2 x2
x 2 x 2 2, 2
4x
1 3x 6
_______________
x 2 x 1 7x 5
______________
x 2 x 1 2
2
x__________________
1 3x 6x 3x 5x 1
______________
x 2 x 2 x 2 x 2 x
3
4x 1
x
2
______________
_____
_____
x 2 x 1 x1 x2
3x
x1
_____________
_____
x2
x 2 x 2 x
2, 1
1 and _________
7
______
9. What is the LCD of 2x
?
2
2
x 9
x x6
x
3 x 3 x 2 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c08-3_rt.indd 23
23
Holt Algebra 2
12/26/05 6:56:34 AM
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