adding & subtracting rational expressions€¦ · steps of add & subtract rational...
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![Page 1: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/1.jpg)
Adding & Subtracting Rational Expressions
9/27/2015 7:22 PM4.3: Add and Subtract Rational Expressions
1
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Example 1
Simplify 5𝑥
2𝑦+
𝑥
2𝑦
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3x
y
6
2
x
y
3
![Page 3: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/3.jpg)
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
![Page 4: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/4.jpg)
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
![Page 5: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/5.jpg)
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?
9/27/2015 7:22 PM 4.3: Add and Subtract Rational Expressions 6
30
29x
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Example 3
Find the LCD of (x + 2) and (x – 2)
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2 2x x
1 1
2 2x x
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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
![Page 9: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/9.jpg)
Your Turn
Find the LCD of (x – 4)2 and (3x – 12)
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2
3 4x
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Example 5
Simplify
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13
24x
7 5
6 8x x 3 4
4 3
24 24x x
28 15
![Page 11: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/11.jpg)
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
![Page 12: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/12.jpg)
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
![Page 13: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/13.jpg)
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
![Page 14: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/14.jpg)
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
![Page 15: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/15.jpg)
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
![Page 16: Adding & Subtracting Rational Expressions€¦ · Steps of Add & Subtract Rational Expressions A. When given an equation, rewrite the fraction using the common denominator. B. Simplify](https://reader034.vdocument.in/reader034/viewer/2022042314/5ee315bead6a402d666d2e1a/html5/thumbnails/16.jpg)
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