1. Addition and Subtraction of Rational Expressions
Section 6.3
Addition and Subtraction of Rational Expressions

2. Objectives Least Common Multiples
Review of Addition and Subtraction of Fractions
Addition of Rational Expressions
Subtraction of Rational Expressions

3. 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.

4. 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.

5. 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.

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

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

8. SUMS OF RATIONAL EXPRESSIONS
To add two rational expressions with like denominators, add their numerators. The denominator does not change.
C not zero

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

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

11. DIFFERENCES OF RATIONAL EXPRESSIONS
To subtract two rational expressions with like denominators, subtract their numerators. The denominator does not change.
C not zero

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

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

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

15. 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.

16. 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