6.4 & 6.5 Adding & Subtracting Rational Expressions

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6.4 6.5 Adding SubtractingRational
Expressions
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Finding Least Common Denominators Monomials

• Find the LCD of the numbers
• List any variable that occurs ANYWHERE in ANY
  denominator
• Give each variable its BIGGEST exponent

3x2 2x5
6
6
x x
5 5
3
4a2b 10ab3
20 20
a b a b
2 3 2 3
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Making Equivalent Expressions
2 5

• Rewrite numerators
• Make new denominators using LCD
• Determine old denom. X ? LCD and multiply
  numerator by ?
• Write new expressions

3x2 2x5
2 5
(2x3)
(3)
6x5 6x5
4x3 15 6x5 6x5
5
5 3
4a2b 10ab3
5 3
(5b2)
(2a)
20a2b3 20a2b3
25b2 6a
20a2b3 20a2b3
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The Whole Process
2 5

• Rewrite numerators
• Make new denominators using LCD
• Make equivalent expressions
• Combine Expressions over One Denominator

3x2 2x5
2 5
(2x3)
(3)

6x5 6x5
4x3 15 6x5 6x5

4x3 15
6x5
7
5 3
-
4a2b 10ab3
5 3
(5b2)
(2a)
-
20a2b3 20a2b3
25b2 6a
-
20a2b3 20a2b3
25b2 6a
20a2b3
8
5 2c
1 6c

(3)
5 1
6c
6c
16 6c
8 3c
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Polynomial Problems

• Factor all polynomials
• LCD is all the different numbers present

3 _ 1
x2 4 x 2
3 _ 1
(x 2)(x 2) (x 2)
3 _ 1
(x 2)
(x 2)(x 2) (x 2)(x 2)
3 1(x 2)
(x 2)(x 2)
-x 5
(x 2)(x 2)
10
4 _ 5 3 x
4 _ 5
x
(3)
3x 3x
4x _ 15
3x 3x
4x 15 3x
11
x 2 4 x 3

(x 2) 4
(x 3)

x 3 x 3
x2 x 6 4

x 3 x 3
x2 x 2 x 3
(x 1)(x 2) x 3
12
3 2

a2 36 6 a
3 2

(a 6)(a 6) 1(a 6)
3 _ 2
(a 6)
(a 6)(a 6) (a 6)(a 6)
3 2a 12
(a 6)(a 6)
- 2a - 9
(a 6)(a 6)
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3x _ 5x x 9x 2
2 9x 81x2 4

3x 5x x
_
9x 2 -1(9x 2) (9x 2)(9x 2)
(9x 2)
(9x 2)
3x 5x
x

(9x 2)(9x 2) (9x 2)(9x 2) (9x
2)(9x 2)
27x2 6x 45x2 10x x
(9x 2)(9x 2)
72x2 5x
(9x 2)(9x 2)
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