1. ALGEBRA – LESSON 93 Quotient of Rational Expressions Be ready to grade the homework!

2. Quotient of Rational Expressions We know that whenever we are multiplying fractions, we can cancel like terms from the top and bottom to simplify the equation before calculating the final answer. We will do the same thing with rational expressions with equations on the top and bottom. 2 3 5 8. 2x 7 6 x. (x+1) 3 6 (x+1).

3. Quotient of Rational Expressions 1) Factor all expressions. a) Pull out common terms. b) “Unfoil” c) Difference of 2 squares. 2) Flip and Cancel all like terms or “bricks”. 3) Multiply Remember: Division problems become multiplication problems by flipping the 2 nd fraction.

4. Quotient of Rational Expressions #1 g 2 + 8g + 16 g 2 + 9g + 20 g 2 - 16 g 2 + 2g - 15  (g + 4)(g + 4) (g + 4)(g + 5) (g + 4)(g - 4) (g + 5)(g - 3)  (g + 4)(g + 4) (g + 4)(g + 5) x (g + 4)(g - 4) (g + 5)(g - 3) = (g - 4) (g - 3)

5. Quotient of Rational Expressions #2 x 2 – x – 12 x 2 + 3x x 2 – 13x + 36 x 3 – 4x 2 – 45x  (x - 4)(x + 3) x(x + 3) (x - 9)(x - 4) x(x + 5)(x - 9)  (x - 4)(x + 3) x(x + 3) x (x - 9)(x - 4) x(x + 5)(x - 9) = (x + 5)

6. Quotient of Rational Expressions #3 p 2 – p – 2 p 2 + 7p + 6 p 2 – 4 p 2 + 7p + 6  (p - 2)(p + 1) (p + 6)(p + 1) (p - 2)(p + 2) (p + 6)(p + 1)  (p - 2)(p + 1) (p + 6)(p + 1) x (p - 2)(p + 2) (p + 6)(p + 1) = (p + 2) (p + 1)

7. Quotient of Rational Expressions #4 m 2 – 10m + 24 m 2 + 3m – 28 m 2 – 36 m 2 + 4m - 21  (m - 6)(m - 4) (m - 4)(m + 7) (m - 6)(m + 6) (m + 7)(m - 3)  (m - 6)(m - 4) (m - 4)(m + 7) x (m - 6)(m + 6) (m + 7)(m - 3) = (m + 6) (m - 3)

8. Homework: Problem Set 93