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Adding & Subtracting Rational Expressions
9/27/2015 7:22 PM4.3: Add and Subtract Rational Expressions
1
Example 1
Simplify 5𝑥
2𝑦+
𝑥
2𝑦
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 2
3x
y
6
2
x
y
3
Example 2
Simplify 3𝑥2+2𝑥
𝑥−1−
10𝑥−5
𝑥−1
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 3
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
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 4
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.
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 5
Review
• What is the common denominator of 6 and 15?
• What is the common denominator of 3x and 9x2?
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 6
30
29x
Example 3
Find the LCD of (x + 2) and (x – 2)
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 7
2 2x x
1 1
2 2x x
Example 4
Find the LCD
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 8
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)
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 9
2
3 4x
Example 5
Simplify
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 10
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?
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 11
3 2x x
3 5
3 2 3 2x x x x
2x 3x
Example 6
Distribute the top.
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 12
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.
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 13
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
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 14
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
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 15
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
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 16
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
