Math 025 Unit 5 Section 6.3.

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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Adding and Subtracting Rational Expressions.

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Presentation transcript:

Math 025 Unit 5 Section 6.3

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

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)

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 3x 2x2 2x2 7x – 3x 2x2 – = 4x 2x2 = 2 x =

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

Objective: To add and subtract fractions with the same denominators. 2x2 + 5 x2 – 3x x – 2 – + x2 + 2x – 3 x2 + 2x – 3 x2 + 2x – 3 2x2 + 5 – x2 + 3x + x – 2 x2 + 2x – 3 = x2 + 4x + 3 x2 + 2x – 3 (x + 3)(x + 1) (x + 3)(x – 1) = = x + 1 x – 1 =

Objective: To add and subtract fractions with different denominators. The LCD = 12x y x 4y 3x 3y 4x 12y 16y 9y – – + + = 12x 12x 12x 12y – 16y + 9y 12x = 5y 12x =

Objective: To add and subtract fractions with different denominators. The LCD = (2x – 3)(x + 1) 2x(x + 1) 1(2x – 3) 2x 1 – – = 2x – 3 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)

Objective: To add and subtract fractions with different denominators. The LCD = (x – 4)(x + 2) x + 3 3 x + 3 3 + = – x2 – 2x – 8 4 – 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)

Objective: To add and subtract fractions with different denominators. The LCD = x2 x2 3 1 + 3 x2 = + 1 x2 x2 x2 + 3 = x2

Objective: To add and subtract fractions with different denominators. 2x 5 2x 5 – = – x – 3 3 – x x – 3 -(x – 3) 2x 5 = + x – 3 x – 3 2x + 5 = x – 3