5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract...
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Transcript of 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract...
![Page 1: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/1.jpg)
5.5 Add and Subtract Rational Expressions
p. 336
What must be true before you can add or subtract complex fractions?
What are two methods to simplify a complex fraction?
![Page 2: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/2.jpg)
Remember: When adding or subtracting fractions, you need a
common denominator!
5
1
5
3 . a
5
4
2
1
3
2 . b
6
3
6
4
6
1
43
21
.c3
4
2
1
6
4
3
2
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Examples:
xxa
2
7
2
3 .
x2
4
x
2
4
6
4
3 .
xx
xb
4
63
x
x4
)2(3
x
xor
![Page 4: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/4.jpg)
The Least Common Multiple (LCM) must be made up of all of the factors of each polynomial, BUT - NO REPEATS
2 2 3Answer
![Page 5: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/5.jpg)
Example:
343 363
4
xx
x
x ** Needs a common denominator 1st!
Sometimes it helps to factor the denominators to make it easier to find
your LCD.)12(33
433
xx
x
xLCD: 3x3(2x+1)
)12(3)12(3
)12(433
xx
x
xx
x
)12(3
)12(43
xx
xx)12(3
493
xx
x
![Page 6: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/6.jpg)
ExampleExample:
9
1
96
122
xxx
x
)3)(3(
1
)3)(3(
1
xxxx
x
)3()3(
)3(
)3()3(
)3)(1(22
xx
x
xx
xx
LCD: (x+3)2(x-3)
)3()3(
)3()3)(1(2
xx
xxx
)3()3(
3332
2
xx
xxxx
)3()3(
632
2
xx
xx
![Page 7: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/7.jpg)
Complex Fraction – a fraction with a fraction in the numerator and/or
denominator.
Such as:
How would you simplify this complex fraction?
Multiply the top by the reciprocal of the bottom!
52
31
6
5
2
5*
3
1
![Page 8: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/8.jpg)
Method 1: Steps to make complex fractions easier
1. Condense the numerator and denominator into one fraction each. (if necessary)
2. Multiply the numerator by the inverse of the denominator.
3. Simplify the remaining fraction.
![Page 9: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/9.jpg)
Method 2: Steps to make complex fractions easier
• Multiply the numerator and the denominator by the least common denominator (LCD) of every fraction in the numerator and denominator.
• Simplify
![Page 10: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/10.jpg)
Method 1: 1 fraction numerator, 1 Method 1: 1 fraction numerator, 1 fraction denominatorfraction denominator
13
41
43
xx
x
)1)(4()4(3
)1)(4()1(
)4(3
xxx
xxx
x
)1)(4(1231
)4(3
xxxx
x
)1)(4(114
)4(3
xxxx
114
)1)(4(
)4(
3
x
xx
x
)114)(4(
)1)(4(3
xx
xx
114
33or
114
)1(3
x
x
x
x
![Page 11: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/11.jpg)
ExampleMethod 1:
xx
x1
14
12
)1()1(
)1(4
12
xxx
xxxx
)1(14
12
xxxx
x
)1(151
2
xxxx
15
)1(
1
2
x
xx
x )15)(1(
)1(2
xx
xx
15
2
x
x
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Method 2: Find LCD Method 2: Find LCD of num. & den.of num. & den.
Simplify:
The LCD of all the fractions in the numerator and denominator is x(x + 4).
5x + 4
1x + 4+ 2
x
5x + 4
1x + 4+ 2
x
=Multiply numerator and denominator by the LCD.
x + 2(x + 4)5x= Simplify.5x
3x + 8=
5x + 4
1x + 4+ 2
x
![Page 13: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/13.jpg)
Method 2
x6
x3
–
x5
710
–
– 5x 3 (2x – 7)=
Multiply numberator and denominator by the LCD (6,3,5 & 10 all factors of 30)
Simplify
x6
x3
–
x5
710
–=
![Page 14: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/14.jpg)
• What must be true before you can add or subtract complex fractions?
The fractions must have common denominators.
• What are two methods to simplify a complex fraction?
Treat the complex fraction as two problems and find the common denominator of each before you invert and multiply or multiply by the LCD of the numerator and denominator.
![Page 15: 5.5 Add and Subtract Rational Expressions p. 336 What must be true before you can add or subtract complex fractions? What are two methods to simplify a.](https://reader035.fdocuments.in/reader035/viewer/2022062515/56649d005503460f949d1993/html5/thumbnails/15.jpg)
5.5 Assignment
p. 340,
3-35 odd