Section 8-4 Multiplying and Dividing Rational Expressions

Objectives I can simplify rational expressions with multiplication I can simplify rational expressions with division

Review Key Concepts Factoring Methods –GCF –Reverse FOIL –Swing & Divide –Difference of 2 Squares

GCF 3x + 9 3(x + 3) Or (2 – x) -1(x – 2)

Reverse FOIL x 2 - x – 12 (x – 4)(x + 3)

Swing & Divide 3x 2 + 2x – 8 x 2 + 2x – 24 (x + 6)(x – 4) (x + 6/3)(x – 4/3) (x + 2)(3x – 4)

Difference of 2 Squares 16x 2 – 9 (4x + 3)(4x – 3)

Multiplying rational Expressions Usually you DON’T multiply, you just reduce 1. You will factor all numerators and denominators, then 2. Reduce or cancel like terms

Simplifying Property for Rational Expressions If a, b, and c are expressions with b and c not equal to zero, then

Example: Reducing

Example: Factoring

EXAMPLE 1 Simplify a rational expression x 2 – 2x – 15 x 2 – 9 Simplify : x 2 – 2x – 15 x 2 – 9 (x +3)(x –5) (x +3)(x –3) = Factor numerator and denominator. (x +3)(x –5) (x +3)(x –3) = Divide out common factor. Simplified form SOLUTION x – 5 x – 3 = ANSWER x – 5 x – 3

GUIDED PRACTICE for Examples 1 and 2 2x x 3x x x x 3x x + 5 (3x + 1)(x + 5) 2x(x + 5) = Factor numerator and denominator. Divide out common factor. 2x2x 3x + 1 = Simplified form (3x + 1)(x + 5) 2x(x + 5) = ANSWER 2x2x 3x + 1 SOLUTION

Dividing Rational Expressions We actually never want to divide rational expressions. Instead, turn them into multiplication problems to simplify by reducing To turn division into multiplication, simply change the sign and invert the 2 nd fraction

Division to Multiplication

Example

Handling Negatives

GUIDED PRACTICE for Examples 6 and 7 Divide the expressions. Simplify the result. 4x4x 5x – 20 x 2 – 2x x 2 – 6x x4x 5x – 20 x 2 – 2x x 2 – 6x + 8 Multiply by reciprocal. Divide out common factors. Factor. Simplified form 4x4x 5x – 20 x 2 – 2x x 2 – 6x + 8 = 4(x)(x – 4)(x – 2) 5(x – 4)(x)(x – 2) = 4(x)(x – 4)(x – 2) 5(x – 4)(x)(x – 2) = 4 5 = SOLUTION

Homework WS 12-4