Adding and Subtracting Rational Expressions 8.2 Adding and Subtracting Rational Expressions

8.2 Adding and Subtracting Rational Expressions Adding or Subtracting Rational Expressions Step 1 If the denominators are the same, add or subtract the numerators. Place the result over the common denominator. If the denominators are different, first find the least common denominator. Write all rational expressions with this LCD, and then add or subtract the numerators. Place the result over the common denominator. Step 2 Simplify. Write all answers in lowest terms. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 1 Adding and Subtracting Rational Expressions with the Same Denominator Add or subtract as indicated. 4m 7 5n + (a) 1 g3 5 – (b) Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 1 Adding and Subtracting Rational Expressions with the Same Denominator a a2 – b2 b – (c) Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 1 Adding and Subtracting Rational Expressions with the Same Denominator Add or subtract as indicated. 5 k2 + 2k – 15 + k (d) Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions The Least Common Denominator Finding the Least Common Denominator Step 1 Factor each denominator. Step 2 Find the least common denominator. The LCD is the product of all different factors from each denominator, with each factor raised to the greatest power that occurs in the denominator. Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 2 Finding Least Common Denominators Assume that the given expressions are denominators of fractions. Find the LCD for each group. (a) 4m3n2, 6m2n5

8.2 Adding and Subtracting Rational Expressions EXAMPLE 3 Adding and Subtracting Rational Expressions with Different Denominators Add or subtract as indicated. The LCD of 3z and 9z is 9z. 3z 7 9z 1 + (a)

8.2 Adding and Subtracting Rational Expressions EXAMPLE 3 Adding and Subtracting Rational Expressions with Different Denominators y 2 y – 4 3 – (b) Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions Caution with Subtracting Rational Expressions d + 5 d – 6 8d –

8.2 Adding and Subtracting Rational Expressions EXAMPLE 4 Using the Distributive Property When Subtracting Rational Expressions e + 2 9 e – 2 2 – Copyright © 2010 Pearson Education, Inc. All rights reserved.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 6 Adding and Subtracting Three Rational Expressions n2 + 3n 2 n + 3 3 + n 4 Add.

8.2 Adding and Subtracting Rational Expressions EXAMPLE 7 Subtracting Rational Expressions Add. a2 + 2a – 3 a – 2 – a2 – 5a + 4 a + 2

8.2 Adding and Subtracting Rational Expressions EXAMPLE 7 Add. a2 + 2a – 3 a – 2 – a2 – 5a + 4 a + 2