simplifying rational expressions we are trying to get common terms to factor ( cancel ) to = 1. you...

Simplifying Rational Expressions

We are trying to get common terms to factor ( cancel ) to = 1. You might have to distribute or FOIL to get started. ALWAYS look to factor 1st….

Simplifying Rational Expressions

22

a

aYou CAN NOT factor terms separated by addition and subtraction.

We are trying to get common terms to factor ( cancel ) to = 1. You might have to distribute or FOIL to get started. ALWAYS look to factor 1st….

REMEMBER !!!

Simplifying Rational Expressions

We are trying to get common terms to factor ( cancel ) to = 1. You might have to distribute or FOIL to get started. ALWAYS look to factor 1st….

REMEMBER !!! 22

a

aYou CAN NOT factor terms separated by addition and subtraction. ONLY multiplication and ONLY terms that are EXACTLY the same !!!

2

4

24

42

a

a

aa

aa

Simplifying Rational Expressions

EXAMPLE : Simplify87

2452

2

xx

xx

Simplifying Rational Expressions

EXAMPLE : Simplify

18

38

87

2452

2

xx

xx

xx

xx

Factor…

Simplifying Rational Expressions

EXAMPLE : Simplify

1

3

18

38

87

2452

2

x

x

xx

xx

xx

xx

Factor…

Cancel…

Simplifying Rational Expressions

EXAMPLE : Simplify 923

172

xx

xx

Simplifying Rational Expressions

EXAMPLE : Simplify

1823

772

923

172

xx

xx

xx

xx

Distribute…

Simplifying Rational Expressions

EXAMPLE : Simplify

185

75

1823

772

923

172

x

x

xx

xx

xx

xx

Distribute…

Combine any like terms…

Simplifying Rational Expressions

EXAMPLE : Simplify

185

75

1823

772

923

172

x

x

xx

xx

xx

xx

Distribute…

Combine any like terms…

This is your answer !!! You CAN NOT cancel the – 5x and 5x

Simplifying Rational Expressions

EXAMPLE : Simplify

h

xhx 22 366

Simplifying Rational Expressions

EXAMPLE : Simplify

h

xhxhx

h

xhx

222

22

361236

366

FOIL ( 6x + h )2

Simplifying Rational Expressions

EXAMPLE : Simplify

h

hxh

h

xhxhx

h

xhx

2

222

22

12

361236

366

FOIL ( 6x + h )2

Combined like terms

Simplifying Rational Expressions

EXAMPLE : Simplify

h

hxh

h

hxh

h

xhxhx

h

xhx

12

12

361236

366

2

222

22

FOIL ( 6x + h )2

Combined like terms

Factored out common term “h”

Simplifying Rational Expressions

EXAMPLE : Simplify

hx

h

hxh

h

hxh

h

xhxhx

h

xhx

12

12

12

361236

366

2

222

22

FOIL ( 6x + h )2

Combined like terms

Factored out common term “h”

Cancel…

Simplifying Rational Expressions

EXAMPLE : Simplify x

xx

412

62

Simplifying Rational Expressions

EXAMPLE : Simplify x

xx

412

62

When simplifying rational expressions, sometimes the order of terms will be reversed.

Simplifying Rational Expressions

EXAMPLE : Simplify x

xx

412

62

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

Simplifying Rational Expressions

EXAMPLE : Simplify x

xx

412

62

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify

xxx

x

xx

34

23

412

62

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify

4

2

34

23

412

62

x

x

xx

x

xx

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify x

xx

212

1832

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify

xxx

x

xx

62

36

212

1832

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify

2

31

62

36

212

1832

x

x

xx

x

xx

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…

Simplifying Rational Expressions

EXAMPLE : Simplify

2

3

2

31

62

36

212

1832

xx

x

xx

x

xx

When simplifying rational expressions, sometimes the order of terms will be reversed.

12

2

x

xWhen the terms are separated by addition, the order really doesn’t matter and still allows you to cancel…

12

2

x

x When the terms are separated by subtraction, the order does matter. You can still cancel but now we need to place a negative sign in our answer…