Chapter 6 Rational Expressions and Equations Section 6.1 Multiplying Rational Expressions.
Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A....
Transcript of Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A....
Adding & Subtracting Rational Expressions
9/27/2015 7:22 PM4.3: Add and Subtract Rational Expressions
1
Example 1
Simplify 5𝑥
2𝑦+
𝑥
2𝑦
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3x
y
6
2
x
y
3
Example 2
Simplify 3𝑥2+2𝑥
𝑥−1−
10𝑥−5
𝑥−1
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3 5x
23 2 10 5
1
x x x
x
23 2 10 5
1
x x x
x
23 8 5
1
x x
x
3 5 1
1
x x
x
Your Turn
Simplify 2𝑥2+5𝑥
𝑥+2−
4𝑥+6
𝑥+2
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2 3x
22 5 4 6
2
x x x
x
22 5 4 6
2
x x x
x
22 6
2
x x
x
2 3 2
2
x x
x
Steps of Add & Subtract Rational Expressions
A. When given an equation, rewrite the fraction using the common denominator.
B. Simplify by combining like terms of both the numerator and denominator.
C. Multiply if needed and then simplify.
D. Reduce to lowest terms up top. Do NOT distribute the bottom.
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Review
• What is the common denominator of 6 and 15?
• What is the common denominator of 3x and 9x2?
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30
29x
Example 3
Find the LCD of (x + 2) and (x – 2)
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2 2x x
1 1
2 2x x
Example 4
Find the LCD
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2 2
1 1
6 3 2t t t t
3 2 1t t t
1
2 3t t 1
1 2t t
1
2 31t t t
3
1
1 2t tt
Your Turn
Find the LCD of (x – 4)2 and (3x – 12)
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2
3 4x
Example 5
Simplify
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13
24x
7 5
6 8x x 3 4
4 3
24 24x x
28 15
Example 6
Simplify 3
𝑥−3+
5
𝑥+2What is the common denominator?
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3 2x x
3 5
3 2 3 2x x x x
2x 3x
Example 6
Distribute the top.
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3 2 5 3
3 2 3 2
x x
x x x x
3 6 5 15
3 2 3 2
x x
x x x x
Example 6
Simplify 3
𝑥−3+
5
𝑥+2
Combine like terms.
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3 6 5 15
3 2 3 2
x x
x x x x
8 9
3 2
x
x x
Example 7Simplify
10𝑥
𝑥2−9−
5
𝑥+3
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5
3x
10 5
3 3 3
x
x x x
10 5
3 3 3 3
x
x x x x
(x-3)
10 5 15
3 3
x x
x x
5 15
3 3
x
x x
5 3
3 3
x
x x
Example 8
• Simplify
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2
5 2 3
3 2x x x
2 2 26 6 6x x x
(6)
10x
(3x)
2
10 12 9
6
x x
x
2
19 12
6
x
x
(2x)
9x12
Your Turn
Simplify 3
𝑥+2−
8
𝑥−2
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5 22
2 2
x
x x
3 8
2 2 2 2x x x x
(x-2) (x+2)
3 6 8 2
2 2
x x
x x
3 6 8 16
2 2
x x
x x