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….


22

a

aYou CAN NOT factor terms separated by addition and subtraction.


REMEMBER !!!



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


EXAMPLE : Simplify87

2452

2

xx

xx


EXAMPLE : Simplify

18

38

87

2452

2

xx

xx

xx

xx

Factor…


EXAMPLE : Simplify

1

3

18

38

87

2452

2

x

x

xx

xx

xx

xx

Factor…

Cancel…


EXAMPLE : Simplify 923

172

xx

xx


EXAMPLE : Simplify

1823

772

923

172

xx

xx

xx

xx

Distribute…


EXAMPLE : Simplify

185

75

1823

772

923

172

x

x

xx

xx

xx

xx

Distribute…

Combine any like terms…


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


EXAMPLE : Simplify

h

xhx 22 366


EXAMPLE : Simplify

h

xhxhx

h

xhx

222

22

361236

366

FOIL ( 6x + h )2


EXAMPLE : Simplify

h

hxh

h

xhxhx

h

xhx

2

222

22

12

361236

366

FOIL ( 6x + h )2

Combined like terms


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”


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…


EXAMPLE : Simplify x

xx

412

62



xx

412

62

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



xx

412

62


12

2

x

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



xx

412

62


12

2

x


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…


EXAMPLE : Simplify

xxx

x

xx

34

23

412

62


12

2

x


12

2

x



EXAMPLE : Simplify

4

2

34

23

412

62

x

x

xx

x

xx


12

2

x


12

2

x




xx

212

1832


12

2

x


12

2

x



EXAMPLE : Simplify

xxx

x

xx

62

36

212

1832


12

2

x


12

2

x



EXAMPLE : Simplify

2

31

62

36

212

1832

x

x

xx

x

xx


12

2

x


12

2

x



EXAMPLE : Simplify

2

3

2

31

62

36

212

1832

xx

x

xx

x

xx


12

2

x


12

2

x


Simplifying Rational Expressions We are trying to get common terms to factor ( cancel ) to = 1. You...

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