Adding and subtracting rational expressions:

1. Adding and subtracting rational expressions: To add or subtract rational expressions use the addition property: Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

2. If the expressions have the same (common) denominator, add or subtract the numerators, keep the same denominator, and simplify the result. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

3. Do the operations and simplify the result: Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

4. =1 Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

5. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

6. =9 Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

7. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

8. To add or subtract fractions with different denominators find the least common denominator (LCD), change each fraction so that it has that denominator then add or subtract Simply stated, the LCD is the least number (expression) that all denominators will divide into evenly. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

9. To find the LCD • factor each denominator • write the different factors • give each factor the highest power to which it occurs • multiply the results Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

10. Factor each write each factor give each highest exponent multiply results (y+4)(y-4) and (y-4)² (y+4)(y-4) (y+4)(y-4)² (y+4)(y-4)² Find the LCD for y²-16 and y²-8y+16 Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

11. Add : • LCD = • change each fraction to LCD • add/subtract • simplify Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

12. Add : • LCD = • change each fraction to LCD • add/subtract • simplify Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

13. Add : • LCD = • change each fraction to LCD • add/subtract • simplify (Top isn’t factorable) Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

14. If the denominators have opposite factors, then change one of them using the 3 signs of a fraction rule. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

15. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

16. 1) 2) 3) 4) Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

17. Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

18. (x+3) (x-2) (x+3)(x-5)(x-5) (x-2) Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

19. (y – 2) (y+2) -(y-2)(y+2)

20. (x-1) (x-1)(x+1) (x+1)(x+1) LCM: (x-1)(x+1)(x+1) Taken from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1