![Page 1: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/1.jpg)
9.5 Addition, Subtraction, and Complex Fractions
5
1
5
3 )1
5
4 2
1
3
2 )2
6
3
6
4
6
1
Do Now:
Obj: to add and subtract rational expressions
Remember: you need a common denominator!
![Page 2: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/2.jpg)
Ex 1:
xxa
2
7
2
3 )
x2
4
x
2
4
6
4
3 )
xx
xb
4
63
x
x4
)2(3
x
xor
![Page 3: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/3.jpg)
Ex 2:
233 363
4)
xx
x
xa
Needs a common denominator 1st
Sometimes it helps to factor the denominators to find your LCD.
)12(33
423
xx
x
x LCD: 3x3(2x+1)
)12(3
)(
)12(3
)12(433
xx
xx
xx
x
)12(3
483
2
xx
xx)12(3
483
2
xx
xx
![Page 4: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/4.jpg)
9
1
96
1)
22
xxx
xb
)3)(3(
1
)3)(3(
1
xxxx
x
)3)(3)(3(
)3(1
)3)(3)(3(
)3)(1(
xxx
x
xxx
xx
LCD: (x+3)(x+3)(x-3)
)3)(3)(3(
3332
xxx
xxxx
)3)(3)(3(
632
xxx
xx
HW:
![Page 5: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/5.jpg)
43
21
.c3
4
2
1
6
4
3
2
Do Now:
![Page 6: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/6.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 7: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/7.jpg)
Steps to make complex fractions easier.
1. Condense the numerator and denominator into one fraction each. (if necessary)
2. Multiply the numerator by the denominator.
3. Simplify the remaining fraction.
![Page 8: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/8.jpg)
Ex 1:Ex 1:
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 9: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/9.jpg)
Ex 2:
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
![Page 10: 9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!](https://reader036.vdocument.in/reader036/viewer/2022082712/56649edb5503460f94beb780/html5/thumbnails/10.jpg)
Ex 3:
31
31
32
94
2
xx
xx
)3(1
)3(1
)3(2
)3)(3(4
xx
xxx
)3)(3()3(
)3)(3()3(
)3)(3()3(2
)3)(3(4
xxx
xxx
xxx
xx
)3)(3()3()3(
)3)(3()3(24
xxxxxxx
)3)(3(2
)3)(3(102
xxxxx
x
x
xx
xx
x
2
)3)(3(
)3)(3(
102
xxx
xxx
2)3)(3(
)3)(3)(102(
x
x
2
102
x
x
2
)5(2
x
x 5