9.1 – multiplying & dividing rational expressions

9.1 – Multiplying & Dividing Rational Expressions

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 12b2

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c 12b2

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c 12b2 6·2·b·b

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c 12b2 6·2·b·b

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c 12b2 6·2·b·b

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c 12b2 6·2·b·b

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2b

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = x2 – 4x – 5

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = x2 – 4x – 5

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5 (x – 5)(x + 1)

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5 (x – 5)(x + 1)

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5 (x – 5)(x + 1)

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5 (x – 5)(x + 1)

9.1 – Multiplying & Dividing Rational Expressions

Ex. 1 Simplify.a. 30bc 12b2

30bc = 6·5·b·c = 5c 12b2 6·2·b·b 2bb. 2x2 – 10x x2 – 4x – 5 2x2 – 10x = 2x(x – 5) x2 – 4x – 5 (x – 5)(x + 1)

= 2x x + 1

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 5b 16a3

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b

2·2·2·2·5·a·a·a·b

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b

2·2·2·2·5·a·a·a·b

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b 2·2·2·2·5·a·a·a·b

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b 2·2·2·2·5·a·a·a·b = 3·b 2·2·a·a

Ex. 2 Simplify each expression.a. 4a . 15b2

5b 16a3

4a . 15b2 = 4a · 15b2 5b 16a3 5b · 16a3

= 2·2·3·5·a·b·b 2·2·2·2·5·a·a·a·b = 3·b = 3b 2·2·a·a 4a2

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 =

x2 + 4x + 3 x – 2

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2)

x2 + 4x + 3 x – 2

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2)

x2 + 4x + 3 x – 2 (x + 3)(x + 1)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

= 3(x + 4) (x + 3)

b. x2 + 2x – 8 . 3x + 3

x2 + 4x + 3 x – 2

x2 + 2x – 8 . 3x + 3 = (x + 4)(x – 2) . 3(x + 1)

x2 + 4x + 3 x – 2 (x + 3)(x + 1) (x – 2)

= 3(x + 4)(x – 2)(x + 1) (x + 3)(x + 1)(x – 2)

= 3(x + 4) = 3x + 12 (x + 3) x + 3

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 15a3b3 5ab3

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y 15a3b3 5ab3 15a3b3

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

2·3·5·a·a·a·b·b·b·x·y·y

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

2·3·5·a·a·a·b·b·b·x·y·y

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

2·3·5·a·a·a·b·b·b·x·y·y

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

2·3·5·a·a·a·b·b·b·x·y·y = 2·x 3·a·a·y

Ex. 3 Simplify each expression.a. 4x2y ÷ 2xy2

15a3b3 5ab3

4x2y ÷ 2xy2 = 4x2y . 5ab3 15a3b3 5ab3 15a3b3 2xy2

= 2·2·5·a·b·b·b·x·x·y

2·3·5·a·a·a·b·b·b·x·y·y = 2·x = 2x 3·a·a·y 3a2y

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 =

x2 – 9 x + 3

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12

x2 – 9 x + 3 x2 – 9

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3

x2 – 9 x + 3 x2 – 9 x + 2

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3

x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3

x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) (x + 3)(x – 3)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3

x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3)

(x + 3)(x – 3) (x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3

x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

b. x2 + x – 12 ÷ x + 2 x2 – 9 x + 3 x2 + x – 12 ÷ x + 2 = x2 + x – 12 . x + 3 x2 – 9 x + 3 x2 – 9 x + 2

= (x + 4)(x – 3) . (x + 3) (x + 3)(x – 3) (x + 2)

= (x + 4)(x – 3)(x + 3)(x + 3)(x – 3)(x + 2)

= x + 4 x + 2