1. Operations on Rational Expressions ADD/SUBTRACT

2. The least common multiple (LCM) of two or more numbers is the least number that contains the prime factorization of each number, or literally the least common multiple they have!! EX1. Find the LCM of 15 and 6. EX2. Find the LCM of 4x 2 + 4x and x 2 + 2x + 1. 4x 2 + 4x = (4x)(x +1) x 2 + 2x + 1 = (x +1)(x +1) LCM = 4x (x +1)(x +1) factors of 4x 2 + 4x factors of x 2 + 2x + 1 15 = (3 5) LCM = 2 3 5 factors of 15 factors of 6 6 = (2 3) = 4x 3 + 8x 2 + 4x = 30 Or: Mults. of 6  6, 12, 18, 24, 30, …Mults. of 15  15, 30, … Multiply what they don’t have in common by what they do have in common, not repeating what they do have in common!

3. LCM Fractions can be expressed in terms of the least common multiple of their denominators. Example: Write the fractions and in terms of the LCM of the denominators…this is how we find common denominators to add or subtract! The LCM of the denominators is 12x 2 (x – 2).

4. 1.If necessary, rewrite the fractions with a common denominator. To add rational expressions: To subtract rational expressions: 2. Add the numerators of each fraction. **Denominator stays the same! 1.If necessary, rewrite the fractions with a common denominator. 2. Subtract the numerators of each fraction. **Denominator stays the same! Don’t forget to distribute the negative if you are subtracting more than one term in the second expression!!

5. Example: Add Example: Subtract

6. Two rational expressions with different denominators can be added or subtracted after they are rewritten with a common denominator. Example: Add

7. Example: Subtract Subtract numerators. Factor. Cancel out. Simplest form.