1. Adding/Subtracting Rationals

2. What do we have to do to add/sub rationals? Simplify each rational first (this will make your life easier later ) To be on safe side : find the excluded values Multiply all denominators to numerators that weren’t there in original Add or subtract Simplify if you can – all done!!

3. Add ex. Ex Can we simplify either of these? No we can’t What are our excluded values? X=0 Now lets do some multiplication : – x * x 2 + 2(2x-1) = x 3 + 4x-2 (same denominator!) 2 * x 2 2*x 2 2x 2 2x 2 Now we can add: x 3 + 4x – 2(all done ) 2x 2

4. Add ex #2 Add 1 st – any common terms? No 2 nd - EVs. x = -1, x = -3 3 rd - 2(x+3) + 3x(x+1)4 th – 2x+6 + 3x 2 + 3x (x+1)(x+3) (x+3)(x+1) x 2 + 4x+3 x 2 + 4x+3 5 th – combine like terms: 3x 2 +5x+6ALL DONE ! x 2 +4x+3

5. One More 1 st ( x+2) + x_2 nd - 1 + x_ x(x+2) x-1 x x-1 3 rd – 1*(x-1) + x * x4 th - x-1 + x 2 _ x*(x-1) x*(x-1) x 2 -x x 2 -x 5 th – x 2 + x – 1 x 2 -x

6. Your Turn Add Solution

7. Subtraction Subtraction is the same thing as addition with one exception: distribute the minus sign FIRST and then do what you do for addition!

8. Subtraction Ex. Subtract: First things first: put parentheses around the second expression and distribute the negative so :

9. Subtract ex cont. Now we do the rest of addition: x + (-2x-1)1 + (-2x-1) x(x+1) x-1 (x+1) (x-1) 1*(x-1) + (x+1)(-2x-1) (x-1) + -2x 2 -3x-1 (x+1)(x-1) (x+1)(x-1) x 2 -1 x 2 -1

10. Subtraction Cont. So our answer would be: Your turn: