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. 2 x 2 – 8 x + 8 = (2)(x 2 – 4 x + 4) = (2)(x – 2) 15 x 2 – 60 = (15)(x 2 – 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) = 30(x – 2)2(x + 2) The least common multiple is 30(x + 2)(x – 2)2. 9 -5

Check understanding 2 A p. 505

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

Check Understanding 3 p. 506

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

Check understanding 4 b p. 506

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

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

Check understanding 5 a – c p. 507

Homework Page 507 # 4, 6, 9, 10 - 26 CH. 9. 3 -9. 4 Quiz next class