Simplifying Rational Expressions What is Rational Expression Warmup

$Warm-up I. Reduce the following fractions in it’s SIMPLEST FORM 1 1. 4 =$

Simplifying Rational Expressions Example 1: (Using GCF) GCF = 2 (2 x +4) x

Simplifying Rational Expressions Example 2: (Using GCF) 3 (y– 5) 3 (y – 5)

Simplifying Rational Expressions Your Turn! (Using GCF) 9 (y + 7) 1. = =

Simplifying by factoring Example 1: “big x method” Factor 2 x + 7 x

Simplifying by factoring Your Turn! “big x method” 5 5 (x– 5) = =

Simplifying by cancelations Example 1: Cancelations 1. 2. 3 x 5 xxxxx = 5

Simplifying Rational Expressions More on Simplifying Rational Expressions At the end of the period,

Warm-up 1. 2. 2. 3. Simplify the following RATIONAL EXPRESSIONS 6 (y+2) (5 y+10)

Simplifying Rational Expressions Example 1 2 x + 7 x + 12 = 2

Simplifying Rational Expressions Example 2 2 4 x GCF = 4 x + 8

Simplifying Rational Expressions Example 3 2 12 x 4 = 2 12 x (

Slides: 13

Download presentation

Simplifying Rational Expressions What is Rational Expression?

$Warm-up I. Reduce the following fractions in it’s SIMPLEST FORM 1 1. 4 =$

Warm-up I. Reduce the following fractions in it’s SIMPLEST FORM 1 1. 4 = 12 3 2. – 15 = – 5 24 8 3. 25 35 = 5 7 II. Factor each of the following quadratics 1. x 2 + 7 x + 12 (x + 3) 2. 2 x + 21 x + 20 (x + 20) 3. 2 x ( x + 4) ( x + 1) - 6 x + 8 (x - 4) ( x - 2)

Simplifying Rational Expressions Example 1: (Using GCF) GCF = 2 (2 x +4) x (x+2) = 2 (x +2) x (x+2) = 2 x

Simplifying Rational Expressions Example 2: (Using GCF) 3 (y– 5) 3 (y – 5) = = (5 y – 25) 5 (y– 5) GCF = 5 3 5

Simplifying Rational Expressions Your Turn! (Using GCF) 9 (y + 7) 1. = = (5 y+35) 5 (y + 7) 9 (3 x + 6) 3 (x +2) 2. = = x (x+2) 3 GCF = 5 GCF = 3 5 x

Simplifying by factoring Example 1: “big x method” Factor 2 x + 7 x + 12 (x + 4)(x + 3) 2 (x+4) = 2 (x+4) (x+3) = 2

Simplifying by factoring Your Turn! “big x method” 5 5 (x– 5) = = 2 x - 7 x + 10 (x - 2)(x – 5) (x-2) 5 (x– 5) Factor

Simplifying by cancelations Example 1: Cancelations 1. 2. 3 x 5 xxxxx = 5 xxx = = 2 25 5 25 xx 25 x 5 5 5 x 2 6 y 4 2 y 6 yy = 2 yyyy 3 6 = 2 yy 3 = 2 y

Simplifying Rational Expressions More on Simplifying Rational Expressions At the end of the period, you should be able to: 1. Simplify Rational expressions 2. Finding factors of quadratic equations

Warm-up 1. 2. 2. 3. Simplify the following RATIONAL EXPRESSIONS 6 (y+2) (5 y+10) 2 x + 12 x + 32 x (x+4) 5 2 3 x y 2 4 9 x y = 6 5 (x+8) = x = 3 x 2 3 y

Simplifying Rational Expressions Example 1 2 x + 7 x + 12 = 2 x (x+3) (x+4) (x+5) (x+3) + 8 x + 15 = (x+4) (x+5) Your Turn 1 2 x - 4 x - 12 2 x -x-6 = (x-6) (x+2) (x-3) (x+2) = (x-6) (x-3)

Simplifying Rational Expressions Example 2 2 4 x GCF = 4 x + 8 x = 2 3 x 4 x (x+2) 3 x (x+2) + 6 x = 4 3 GCF = 3 x Your Turn 2 7 x GCF = 7 x – 35 x = 2 3 x – 15 x GCF = 3 x 7 x (x - 5) 3 x (x - 5) = 7 3

Simplifying Rational Expressions Example 3 2 12 x 4 = 2 12 x ( 3 x + 6 ) 3 ( x+2 ) = 2 4 x x+2 GCF = 3 Your Turn! 2 12 x 2 (4 x – 6 x ) GCF = 2 x 6 x = 2 12 x 2 x ( 2 x – 3 ) = 6 x 2 x - 3