simplifying rational expressions we are trying to get common terms to factor ( cancel ) to = 1. you...
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![Page 1: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/1.jpg)
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….
![Page 2: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/2.jpg)
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 !!!
![Page 3: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/3.jpg)
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
![Page 4: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/4.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify87
2452
2
xx
xx
![Page 5: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/5.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
18
38
87
2452
2
xx
xx
xx
xx
Factor…
![Page 6: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/6.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
1
3
18
38
87
2452
2
x
x
xx
xx
xx
xx
Factor…
Cancel…
![Page 7: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/7.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify 923
172
xx
xx
![Page 8: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/8.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
1823
772
923
172
xx
xx
xx
xx
Distribute…
![Page 9: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/9.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
185
75
1823
772
923
172
x
x
xx
xx
xx
xx
Distribute…
Combine any like terms…
![Page 10: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/11.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
h
xhx 22 366
![Page 12: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/12.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
h
xhxhx
h
xhx
222
22
361236
366
FOIL ( 6x + h )2
![Page 13: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/13.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify
h
hxh
h
xhxhx
h
xhx
2
222
22
12
361236
366
FOIL ( 6x + h )2
Combined like terms
![Page 14: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/14.jpg)
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”
![Page 15: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/15.jpg)
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…
![Page 16: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/16.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify x
xx
412
62
![Page 17: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/17.jpg)
Simplifying Rational Expressions
EXAMPLE : Simplify x
xx
412
62
When simplifying rational expressions, sometimes the order of terms will be reversed.
![Page 18: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/18.jpg)
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…
![Page 19: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/19.jpg)
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…
![Page 20: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/20.jpg)
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…
![Page 21: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/21.jpg)
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…
![Page 22: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/22.jpg)
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…
![Page 23: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/23.jpg)
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…
![Page 24: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/24.jpg)
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…
![Page 25: 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](https://reader036.vdocuments.us/reader036/viewer/2022062619/5516e55f55034603568b46e7/html5/thumbnails/25.jpg)
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…