1. Adding & Subtracting Rational Expressions

2. Finding Least Common Denominators: Monomials Find the LCD of the numbers List any variable that occurs ANYWHERE in ANY denominator Give each variable its BIGGEST exponent 3x 2 2x 5 66x 5

3. 4a 2 b 10ab 3 20 a b 2 3

4. Making Equivalent Expressions Rewrite numerators Make new denominators using LCD Determine: old denom. X ? = LCD and multiply numerator by ? Write new expressions 3x 2 2x 5 2 5 6x 5 (2x 3 )(3) 4x 3 15 6x 5

5. 4a 2 b 10ab 3 5 3 20a 2 b 3 (5b 2 )(2a) 20a 2 b 3 25b 2 6a

6. Adding/Subtracting Rewrite numerators Make new denominators using LCD Make equivalent expressions Combine Expressions over One Denominator 3x 2 2x 5 2 5 6x 5 (2x 3 )(3) 4x 3 15 6x 5 + + + 4x 3 + 15

7. 4a 2 b 10ab 3 5 3 20a 2 b 3 (5b 2 )(2a) 20a 2 b 3 25b 2 6a - - - 20a 2 b 3 25b 2 – 6a

8. 5 2c + 1 6c 5 + 1 6c (3) 16 6c 8 3c

9. Polynomial Problems Factor all polynomials LCD is all the different “numbers” present x 2 – 4 x + 2 3 _ 1 (x + 2)(x – 2) (x + 2) 3 _ 1 (x + 2)(x – 2) (x – 2) (x + 2)(x – 2) 3 – 1(x – 2) (x + 2)(x – 2) -x + 5

10. 4 _ 5 3 x 4 _ 5 3x x(3) 3x 4x _ 15 4x – 15 3x

11. x + 2 4 x – 3 + + (x + 2) 4 x – 3 (x – 3) x – 3 + x 2 – x – 6 4 x 2 – x – 2 x – 3 (x + 1)(x – 2) x – 3

12. a 2 – 36 a – 6 + 3 2 (a + 6)(a – 6) (a – 6) + 3 2 3 + 2 (a + 6)(a – 6) (a + 6) (a + 6)(a – 6) 3 + 2a + 12 (a + 6)(a – 6) 2a + 15

13. 3x _ 5x x 9x + 2 9x + 2 81x 2 – 4 + 3x 5x x 9x + 2 (9x – 2) (9x + 2)(9x – 2) _ + 3x 5x x - + (9x + 2)(9x – 2) (9x + 2)(9x – 2) (9x + 2)(9x – 2) (9x – 2)(9x + 2) 27x 2 – 6x - 45x 2 - 10x + x (9x + 2)(9x – 2) -18x 2 - 15x