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CH. 9.5 Adding and Subtracting Rational Expressions

CH. 9.5 Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions. ALGEBRA 2 LESSON 9-5. Find the least common multiple of 2 x 2 – 8 x + 8 and 15 x 2 – 60. Step 1:   Find the prime factors of each expression.

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CH. 9.5 Adding and Subtracting Rational Expressions

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  1. CH. 9.5 Adding and Subtracting Rational Expressions

  2. Adding and Subtracting Rational Expressions ALGEBRA 2 LESSON 9-5 Find the least common multiple of 2x2 – 8x + 8 and 15x2 – 60. Step 1:  Find the prime factors of each expression. 2x2 – 8x + 8 = (2)(x2 – 4x + 4) = (2)(x – 2)(x – 2) 15x2 – 60 = (15)(x2 – 4) = (3)(5)(x – 2)(x + 2) Step 2: Write each prime factor the greatest number of times it appears in either expression. Simplify where possible. (2)(3)(5)(x – 2)(x – 2)(x + 2) = 30(x – 2)2(x + 2) The least common multiple is 30(x + 2)(x – 2)2. 9-5

  3. Check understanding 2A p. 505

  4. 1 3(x + 2)(x + 5) 1 + 4x(x + 2) 3(x + 2)(x + 5) 4x(x + 2) 3(x + 2)(x + 5) 1 3(x + 2)(x + 5) 1 3(x + 2)(x + 5) 4x2 + 8x +1 3(x + 2)(x + 5) 1 3x2 + 21x +30 1 3x2 + 21x +30 4x2 + 8x +1 3x2 + 21x +30 4x 3(x + 5) 4x 3x + 15 + = + Factor the denominators. 4x 3(x + 5) = + • Identity for Multiplication. = + Multiply. x + 2 x + 2 = Add. = Simplify the numerator. = Simplify the denominator. Adding and Subtracting Rational Expressions ALGEBRA 2 LESSON 9-5 4x 3x + 15 Simplify + . 9-5

  5. Check Understanding 3 p. 506

  6. 2x (x – 3)(x + 1) 2x (x – 3)(x + 1) 2x x2 – 2x – 3 2x x2 – 2x – 3 3 4x + 4 Simplify - . 3 4x + 4 3 4(x + 1) – = – Factor the denominators. 3 4(x + 1) = • – • Identity for Multiplication. 4(2x) – [(3)(x – 3)] 4(x + 1)(x – 3) = Simplify. 4 4 5x + 9 4x2 – 8x – 12 x – 3 x – 3 = Simplify. Adding and Subtracting Rational Expressions ALGEBRA 2 LESSON 9-5 9-5

  7. Check understanding 4b p. 506

  8. 1 x 1 y 1 x 1 y + + • xy = The LCD is xy. Multiply the numerator and denominator by xy. 1 • xy y 1 • xy x 2 y 1 x 2 y 1 x + – – • xy 1 • xy x 2 • xy y – = Use the Distributive Property. y + x 2x – y = Simplify. Adding and Subtracting Rational Expressions ALGEBRA 2 LESSON 9-5 1 x 1 y + Simplify . 2 y 1 x – Method 1: First find the LCD of all the rational expressions. 9-5

  9. x + y xy x + y xy x + y xy 1 x 1 y y xy x xy + + = Write equivalent expressions with common denominators. 2x xy x xy 2x – y xy xy 2x – y 2x – y xy 2 y 1 x – – = Add. = ÷ Divide the numerator fraction by the denominator fraction. = • Multiply by the reciprocal. x + y 2x – y = Adding and Subtracting Rational Expressions ALGEBRA 2 LESSON 9-5 (continued) Method 2: First simplify the numerator and denominator. 9-5

  10. Check understanding 5 a – c p. 507

  11. Homework Page 507 # 4, 6, 9, 10 - 26 CH. 9.3-9.4 Quiz next class

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