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Math 025 Unit 5 Section 6.3

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The LCM of two expressions is the product of the largest powers of the factors that occur in any one factorization of the expressions Examples: 18 = 2 · 32 The LCM of 12 and 18 is 22 · 32 = 36 12 = 22 · 3 6x3 = 2·3·x3 The LCM is 23·3·x3 12x = 22·3· x = 24x3 8x2 = 23·x2

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**Find the LCM of the following:**

x + 3 x – 2 x2 + x – 6 = (x + 3)(x – 2) LCM = (x + 3)(x – 2) x2 – 5x – 14 = (x – 7)(x + 2) x2 – 4 = (x – 2)(x + 2) LCM = (x – 7)(x – 2)(x + 2)

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**Objective: To add and subtract fractions with the same denominators.**

1. Keep the same denominator for the answer 2. Add or subtract the numerators as indicated 3. Simplify the answer if possible 7x x x x2 7x – 3x x2 – = 4x 2x2 = x =

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**Objective: To add and subtract fractions with the same denominators.**

1. Keep the same denominator for the answer 2. Add or subtract the numerators as indicated 3. Simplify the answer if possible 3x2 x2 – 1 x + 4 x2 – 1 – 3x2 – x – x2 – 1 = (3x – 4)(x + 1) = (x + 1)(x – 1) 3x – 4 = x – 1

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**Objective: To add and subtract fractions with the same denominators.**

2x2 + 5 x2 – 3x x – 2 – + x2 + 2x – x2 + 2x – x2 + 2x – 3 2x2 + 5 – x2 + 3x + x – x2 + 2x – 3 = x2 + 4x x2 + 2x – 3 (x + 3)(x + 1) (x + 3)(x – 1) = = x x – 1 =

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**Objective: To add and subtract fractions with different denominators.**

The LCD = 12x y x 4y 3x 3y 4x 12y 16y 9y – – + + = 12x x x 12y – 16y + 9y x = 5y x =

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**Objective: To add and subtract fractions with different denominators.**

The LCD = (2x – 3)(x + 1) 2x(x + 1) 1(2x – 3) 2x – – = 2x – x + 1 (2x – 3)(x + 1) (2x – 3)(x + 1) 2x(x + 1) – 1(2x – 3) (2x – 3)(x + 1) = 2x2 + 2x – 2x + 3 (2x – 3)(x + 1) = 2x2 + 3 = (2x – 3)(x + 1)

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**Objective: To add and subtract fractions with different denominators.**

The LCD = (x – 4)(x + 2) x x + = – x2 – 2x – – x (x – 4)(x + 2) x – 4 x + 3 3(x + 2) = – (x – 4)(x + 2) (x – 4)(x + 2) x + 3 – 3(x + 2) (x – 4)(x + 2) x + 3 – 3x – 6 (x – 4)(x + 2) = = - 2x – 3 = (x – 4)(x + 2)

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**Objective: To add and subtract fractions with different denominators.**

The LCD = x2 x2 3 x2 = + 1 x x2 x2 + 3 = x2

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**Objective: To add and subtract fractions with different denominators.**

2x 2x – = – x – – x x – (x – 3) 2x = + x – 3 x – 3 2x + 5 = x – 3

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