1. Adding and subtracting rational expressions:
To add or subtract rational expressions use the addition property:

2. If the expressions have the same (common) denominator, add or subtract the numerators, keep the same denominator, and simplify the result.

3. Do the operations and simplify the result:

4. =1

6. =9

9. Simply stated, the LCD is the least
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.

10. factor each denominator write the different factors
To find the LCD
factor each denominator
write the different factors
give each factor the highest power to which it occurs
multiply the results

11. Find the LCD for y²-16 and y²-8y+16
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

12. change each fraction to LCD
Add :
LCD =
change each fraction to LCD
add/subtra ct
simplify

13. change each fraction to LCD
Add :
LCD =
change each fraction to LCD
add/subtra ct
simplify

14. change each fraction to LCD
Add :
LCD =
change each fraction to LCD
add/subtra ct
simplify
(Top isn’t factorable)

15. If the denominators have opposite factors, then change one of them using the 3 signs of a fraction rule.

17. 1) 2) 3) 4)

19. (x+3) (x-2) (x+3) (x-5) (x-5) (x-2)

20. (y – 2) (y+2) (y-2)(y+2)

21. (x-1) (x-1)(x+1) (x+1)(x+1)
LCM: (x-1)(x+1)(x+1)