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8.3Add and subtract Rational
Expressions
• To Add and SubtractA. Find Common Denominators
B. Combine Like Terms
C. Factor/Simplify
Add and Subtract with Like Denominators
• Example 1
3 4 2 5
3 3
x x
x x
3 4 2 5
3
x x
x
5 1
3
x
x
3 4 2 5
3
x x
x
Add and Subtract with Like Denominators
• Example 2
2 2
2 1 4 4
2 2
x x
x x
2
2 1 4 4
2
x x
x
2
2 1 4 4
2
x x
x
2
2 5
2
x
x
Add and Subtract with Like Denominators
• Example 3
4 3 4 3
2 5 2 5
x x
x x
4 3 4 3
2 5
( ) ( )x x
x
4 3 4 3
2 5
x x
x
6
2 5x
Find the Least Common Multiple of Polynomials
Example 4
Find the least common multiple for each pair.
A. 4x2y3 and 6x4y5 B. x2 – 2x – 3 and x2 – x – 6
4 512x y 3 1x x 3 2x x
1 23 xxx
Find the Least common Multiple of Polynomials
C. D. 3 4 5 32 3x y and x y 2 24 5 6x and x x
5 46x y
2x
2 2 2 3x x and x x
Factor each polynomial FIRST
3x 2x
Add and SubtractExample 5
6 6x x 3 5x x 2 4
6x
23 15 8x x
5 4
2 3
x
x
(3x) (2)
Add and SubtractExample 6
10 10x x 5 3 2 2
10x
15 4
3 2
2 5x x
(5) (2)
19
10x
SubtractExample 8
7
7 2
x
x x 4
7x
7 2 7 2x x x x
7x 4 2x
7 2x x 7 4 2x x
7 4 8
7 2
x x
x x
3 8
7 2
x
x x
2
7 4
9 14 7
x
x x x
Add and SubtractExample 9
6 7 6 7x x
5 7x 6 5x
6 7x 5 7 6 5x x
5 5
6 7
x
x
(x-7) (6) 6 7x 5 35 6 30x x
11 65
6 7
x
x
Add and SubtractExample 10
3 3
2 1 3 1
2x x
x x
9x 6 4x
15 4
6 1
x
x
3 3 2
2 2 3 3
x x
x x
6 1 6 1x x
3 3
2 2
Add and Subtract
x – 3 x2 + 3x – 4
+ 2x x + 4
Example 11
3
1 4
x
x x
2
4
x
x
1 4 1 4x x x x
3x 2 1x x
1 4x x
23 2 2x x x
22 3
1 4
x x
x x
2 3 1
1 4
x x
x x
Add and SubtractExample 12
2x
x 8
2 2x x
2 2 2 2x x x x
2x x 8
2 2x x
2 2 8x x
4 2
2 2
x x
x x
x x + 2
– 8 x2 – 4
4
2
x
x
SubtractExample 13
22 30
3 3
x
x x
5
3
x
x
3 3 3 3x x x x
22 30x 5 3x x
3 3x x 2 22 30 2 15x x x
2 22 30 2 15
3 3
x x x
x x
5
3
x
x
2
2
2 30 5
9 3
x x
x x
2 2 15
3 3
x x
x x
5 3
3 3
x x
x x
3x
3x
SubtractExample 14
2 5 5 2 2 5 5 2x x x x
3 2 5 2x x 2 2 5x
215 16 4x x 2 2 5x
215 16 4 4 10
2 5 5 2
x x x
x x
2 5 5 2x x
3 2 2
2 5 5 2
x
x x
215 20 6
2 5 5 2
x x
x x
5 2x
5 2x
2 5x
2 5x
Add and SubtractExample 7
3 312 12x x 21 4x 5 3
312x
24 15x
3
1 5
3 4x x
(4x²) (3)
Example 15
2
2
2 64 4
64 8
x x
x x
Add Fractions2 3
6 10
30
10 9
30
2 5 3 3
(5) (3)
19
30
