Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)
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Transcript of Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)
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Warm Up #13
1 (6x3 + 12x2 – 18x) 3x
2 (4x2 + 9x +2) (x+2)
3 (x3 + 216) (x + 6)
![Page 2: Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)](https://reader036.fdocuments.us/reader036/viewer/2022082600/5a4d1b2e7f8b9ab059999ff5/html5/thumbnails/2.jpg)
Warm Up #13:
1 (6x3 + 12x2 – 18x) 3x
2 (4x2 + 9x +2) (x+2)
3 (x3 + 216) (x + 6)x2 – 6x +36
4x + 1
2x2 + 4x - 6
![Page 3: Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)](https://reader036.fdocuments.us/reader036/viewer/2022082600/5a4d1b2e7f8b9ab059999ff5/html5/thumbnails/3.jpg)
Complex Rational Expressions
3
21x
13
243
xx
x
yx
x
x
23
281
Fractions inside of fractions are a NO - NO
And must be simplified.
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To simplifyComplex Rational Expressions
• Multiply the numerator and denominator by a fraction equivalent to “1”
• The fraction should contain the factors of all denominators in the expression
8
243
x
x
88
xx46
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Complex Rational Expressions• Multiply the numerator and denominator
by a fraction equivalent to “1”• The fraction should contain the factors
of all denominators in the expression
211
11
x
x
2
2
xx
12
2
xxx
111
xx
xx
1xx
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Steps
1. Find the LCD of the numerator and denominator
2. Multiply the complex rational expression by the LCD/LCD (so its equivalent to multiplying by 1)
3. Simplify (factor and cross out common factors)
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xx
1
5xx
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21
32xx
35x
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8/5
![Page 10: Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)](https://reader036.fdocuments.us/reader036/viewer/2022082600/5a4d1b2e7f8b9ab059999ff5/html5/thumbnails/10.jpg)
yy
2
11
yy
1
1 1y
y y
11y
![Page 11: Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)](https://reader036.fdocuments.us/reader036/viewer/2022082600/5a4d1b2e7f8b9ab059999ff5/html5/thumbnails/11.jpg)
Short Cut
• If there are 2 terms or more on either the numerator or denominator you must multiply by the LCD/LCD
• However, if there is only 1 term on the numerator and 1 term on the denominator then you can divide fractions (which means multiply by the reciprocal)
![Page 12: Warm Up #13 1 (6x 3 + 12x 2 – 18x) 3x 2 (4x 2 + 9x +2) (x+2) 3 (x 3 + 216) (x + 6)](https://reader036.fdocuments.us/reader036/viewer/2022082600/5a4d1b2e7f8b9ab059999ff5/html5/thumbnails/12.jpg)
2
1223
xxxx
123xx
21223
xx
xx
xx
xx2
1223
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Assignment:
Page 4702-27 odd