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**Addition and Subtraction of Rational Expressions**

Section 6.3 Addition and Subtraction of Rational Expressions

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**Objectives Least Common Multiples**

Review of Addition and Subtraction of Fractions Addition of Rational Expressions Subtraction of Rational Expressions

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**FINDING THE LEAST COMMON MULTIPLE**

The least common multiple (LCM) of two or more polynomials can be found as follows. Step 1: Factor each polynomial completely. Step 2: List each factor the greatest number of times that it occurs in either factorization. Step 3: Find the product of this list of factors. The result is the LCM.

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Example Find the least common multiple of each pair of expressions. a. 6x, 9x4 b. x2 + 7x + 12, x2 + 8x + 16 Solution Step 1: Factor each polynomial completely. 6x = 3 ∙ 2 ∙ x 9x4 = 3 ∙ 3 ∙ x ∙ x ∙ x ∙ x Step 2: List each factor the greatest number of times. 3 ∙ 3 ∙ 2 ∙ x ∙ x ∙ x ∙ x Step 3: The LCM is 18x4.

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Example (cont) b. x2 + 7x + 12, x2 + 8x + 16 Step 1: Factor each polynomial completely. x2 + 7x + 12 = (x + 3)(x + 4) x2 + 8x + 16 = (x+ 4)(x + 4) Step 2: List each factor the greatest number of times. (x + 3), (x + 4), and (x + 4) Step 3: The LCM is (x + 3)(x + 4)2.

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Example Find the sum. a. b. Solution a. The LCD is 42. b. The LCD is 18.

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Example Find the difference. a. b. Solution a. The LCD is 36. b. The LCD is 60.

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**SUMS OF RATIONAL EXPRESSIONS**

To add two rational expressions with like denominators, add their numerators. The denominator does not change. C not zero

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Example Add and simplify. a. b. Solution a. b.

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Example Add and simplify. a. b. Solution

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**DIFFERENCES OF RATIONAL EXPRESSIONS**

To subtract two rational expressions with like denominators, subtract their numerators. The denominator does not change. C not zero

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Example Subtract and simplify. a. b. Solution a. b.

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Example Subtract and simplify. Solution The LCD is x(x + 7).

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Example Simplify the expression. Write your answer in lowest terms and leave it in factored form. Solution

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**STEPS FOR FINDING SUMS AND**

DIFFERENCES OF RATIONAL EXPRESSIONS Step 1: If the denominators are not common, multiply each expression by 1 written in the appropriate form to obtain the LCD. Step 2: Add or subtract the numerators. Combine like terms. Step 3: If possible, simplify the final expression.

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Example A 75-watt light bulb with a resistance of R1 = 160 ohms and a 60-watt light bulb with a resistance of R2 = 240 ohms are placed in an electrical circuit. Find the combined resistance. Solution R = 96 ohms

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