1. Multiply 1) 2) Divide 3) 4)

2. Objectives: You will be able to… Add and subtract rational expressions

3.  Same denominator: Add (or subtract) the numerators, keep the denominator the same.  Different denominators: Convert them both to the least common denominator, then add/subtract the numerators, keeping the new denominators the same.  Always reduce if possible at the end.

4.  First we break the denominators into their prime factors.  Every factor needs to be represented in our common denominator…  …so it needs to have a factor of 7,a factor of 3, and a two factors of 2.  Our common denominator will be 2 2 ∙3∙7=84  When our denominators were 3 and 6, finding the LCD was easy. 7 is prime so there are no factors

15.  Just like with fractions, if they have the same denominator already, we can just add or subtract the numerators  Make sure to simplify at the end!  Examples: 1. 2.

16. 1. Find LCD 2. Write each with the LCD by multiplying the numerator and denominator of each by the factors that were missing. 3. Subtract the fractions, leaving the denominator the same

17. Factor denominators: Find LCD: Write both with LCD by multiplying the numerator and denominator of each by what they need. (Remember to distribute!) Add This one needs a 2x +1This one needs another x

18. 1. Find the least common denominator! You might need to factor each denominator first… 2. Figure out what each fraction is missing and multiply the numerator and denominator of each by the missing piece(s). Leave denominator in factored form! 3. Simplify each numerator (FOIL, distribute, combine like terms, etc). 4. Add or subtract the numerators. 5. Factor the numerator to simplify, if possible.

23.  What does the fraction bar mean?  Division  And what do we do when we divide fractions?  Flip the second fraction and multiply  WE ALREADY KNOW HOW TO DO THIS!

25.  1. Define your big fraction bar.  2. Rewrite top fraction.  3. Flip bottom fraction to multiply by the reciprocal.  4. Simplify

26.  Start by looking at the numerator and denominator separately.  Follow our steps from previous classes to make the numerator and denominator each one fraction.  Then follow your steps for dividing fractions (flip the bottom and multiply).

27.  Step 1: Clearly separate numerator and denominator  Step 2: Add/subtract the numerator (if necessary) by following our previous steps.  Step 3: Add/subtract the denominator (if necessary) by following our previous steps.  Step 4: Write the new numerator over the new denominator.  Step 5: Divide the fractions by flipping the fraction in the denominator and multiplying.

28.  Hint #1: Focus on just the top to start  Hint #2: Write the 8 as a fraction over 1

29.  Remember, work on the top and bottom separately, then combine to divide.