1. Section 6.3 Addition, Subtraction, and Least Common Denominator

2. Like Denominators To add/subtract rational expressions with like denominators, we 1) Add/Subtract their numerators 2) Write the sum/difference over the common denominator 3) Simplify the result (Factor before canceling common factors) where A, B, D are polynomials

3. Example Add Combine like terms 1 20 Add the numerators Over the same denominator

4. Example Subtract Factor the numerator 1 1 Subtract the numerators Over the same denominator

5. Example Add Factor 1 1 Add the numerators Over the same denominator Combine like terms

6. Example Subtract Factor 1 1 Subtract the numerators Over the same denominator Combine like terms

7. Example Subtract Factor 1 1 Subtract the numerators Over the same denominator Combine like terms Distribute the negative sign

8. Add or subtract as indicated

9. The Least Common Denominator Finding the Least Common Denominator Step 1 Factor each denominator completely. 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.

10. Example Find the LCD Factor each denominator. 2 2 · m 3 · n 2 2 · 3 · m 2 · n 5 LCD = 2 2 · 3 · m 3 · n 5 = 12 m 3 n 5 Choose the factors with the greatest exponents. 4 m 3 n 2, 6 m 2 n 5

11. Example Find the LCD Factor the denominators. w 2 – 3 w + 2 = (w – 2)(w – 1) w 2 – 4 = (w – 2)(w + 2) LCD = (w – 2)(w – 1)(w + 2)

12. Example Find the LCD Factor the denominators. 15(x – 1) 2 = 3 ∙ 5 ∙ ( x – 1) 2 3x 2 – 3x = 3 ∙ x ∙ ( x – 1) LCD = 3 ∙ 5 ∙ x ∙ ( x – 1) 2 = 15 x ( x – 1) 2

13. Example Find the LCD We cannot factor each denominator further! a +3= a + 3 a – 2 = a – 2 LCD = ( a – 2)( a + 3)

14. Find the LCM of the following polynomials.

15. Building Equivalent Expressions