Simplifying Rational Expressions

Simplifying Rational

ExpressionsWhat is Rational Expression?

Warm-upI. Reduce the

following fractions in it’s

SIMPLEST FORM4

12=

1

3

1.

15

24=2. –

5

8–

25

35=

5

7

3.

II. Factor each of the following quadratics

1. x2 + 7x + 12

(x + 3) ( x + 4)

2. x2 + 21x + 20

(x + 20) ( x + 1)

3. x2 - 6x + 8

(x - 4) ( x - 2)

Simplifying Rational Expressions

Example 1: (Using GCF)

(2x +4)

x (x+2)

2 (x +2)

x (x+2)= =

2

x

GCF = 2


Example 2: (Using GCF)

(5y –25)

3 (y–5) 3 (y –5)

5 (y–5)= =

3

5GCF = 5


Your Turn! (Using GCF)

(5y+35)

9 (y+7) 9 (y + 7)

5 (y + 7)= =

9

5GCF = 5

(3x + 6)

x (x+2)

3 (x +2)

x (x+2)= =

3

x

GCF = 3

1.

2.

2 (x+4)

Simplifying by factoring

x2 + 7x + 12= =

(x+3)

2

Example 1: “big x method”

2 (x+4)

(x + 4)(x + 3)Factor

5 (x–5)

(x - 2)(x – 5)

Simplifying by factoring

x2 - 7x + 10= = (x-

2)

5

Your Turn! “big x method”

5 (x–5)

Factor

Simplifying by cancelations

Example 1: Cancelations

5x5

25x2

1. =5xxxxx

25xx5xxx25

=

5

x3

5=

6y2

2y4

2. =6yy2yyyy

62yy

=3

y2= 3

Simplifying Rational

ExpressionsMore 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

(5y+10)6 (y+2)

=6

51.

Simplify the following RATIONAL

EXPRESSIONS

x2 + 12x + 32 =

(x+8)xx (x+4)

2.

3x5y2

9x2y4

2. 3y2

=x33.


Example 1

x2 + 7x + 12

x2 + 8x + 15=(x+3) (x+4)

(x+5) (x+3)=

(x+4

)(x+5)

Your Turn 1

x2 - 4x - 12

x2 - x - 6=(x-6) (x+2)

(x-3) (x+2)=

(x-6)

(x-3)


Example 2

4x2 + 8x

3x2 + 6x=

4x (x+2)

3x (x+2)=

4

3

GCF = 4x

GCF = 3x

Your Turn

7x2 – 35x

3x2 – 15x=

7x (x - 5)

3x (x - 5)=

7

3

GCF = 7x

GCF = 3x


Example 3

12x2

3x + 6 =

12x2

3 ( x+2 )=

4x2

x+2 GCF = 3

4

( 3x + 6 )

=12x2

2x ( 2x – 3 )=

6x

2x - 3GCF = 2x

6Your Turn!

12x2

(4x2 – 6x )

x

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Simplifying Rational Expressions