PARTIAL FRACTIAN
BA 501 ENGINEERING MATH 4
PARTIAL FRACTION
LINEAR FACTOR
xx
x
211
3
x
B
x
A
211
To find A and B
BxBAxA
xx
xBxA
2
211
121
Equal to 3X xBABAx
BxBAxAx
23
23
)2...(32
)1.....(0
BA
BA
Using calculator >>
mode>> eqn>>
unknown
a1=1,a2=1,c1=0
b1=2,b2=-1,c2=3
1,1 BA
xxxx
x
21
1
1
1
211
3
LINEAR FACTOR
43
11
xx
x
43
x
B
x
A
To find A and B
BBxAAx
xx
xBxA
34
43
34
Equal to X-11 xBABAx
BBxAAxx
3411
3411
)2.......(1
)1.....(1134
BA
BA
Using calculator
>> mode>>
eqn>> unknown
a1=-4,a2=3,
c1=-11
b1=1,b2=1,c2=1
1,2 BA
4
1
3
2
43
11
xxxx
x
LINEAR FACTOR LINEAR FACTOR
2121
2
xxx
x
2121
x
C
x
B
x
A
To find A,B & C
CCxCxBBxBxAAxAx
xxCxxBxxA
xxx
xxCxxBxxA
222
222
22232
122232
2121
12121212
Equal to 2X 2
222
223222
222322
xCBAxCBACBAx
CCxCxBBxBxAAxAxx
)3.......(022
)2.........(23
)1.......(022
CBA
CBA
CBA
Using calculator
>> mode>>
eqn>> unknown
(3)
3
4,
3
4,
3
2 CBA
xxxx
x
21
1
1
1
211
3
LINEAR FACTOR
45
32
xx
x
25
122 x
x
xxx
x
432
104
REPEATED LINEAR FACTOR
23
1
x
x
233
x
B
x
A
To find A and B
BAAx
x
BxA
3
3
32
Equal to X+1 AxBAx
BAAxx
31
31
)2.......(1
)1.....(13
A
BA
Using calculator
>> mode>>
eqn>> unknown
2,1 BA
223
2
3
1
3
1
xxx
x
REPEATED LINEAR FACTOR
227
1435
x
x
22727
x
B
x
A
To find A and B
BAAx
x
BxA
27
27
272
Equal to 35X-14 AxBAx
BAAxx
721435
271435
)2.......(357
)1.....(142
A
BA
Using calculator
>> mode>>
eqn>> unknown
4,5 BA
2227
4
27
5
27
1435
xxx
x
REPEATED LINEAR FACTOR
32
2
1
x
x
32222
x
C
x
B
x
A
To find A, B & C
CBBxAAxAx
CxBxxA
x
CxBxA
244
244
2
22
2
2
3
2
Equal to X2+1 CBAxBAxAx
CBBxAAxAxx
2441
2441
22
22
)3.....(124
)2.......(04
)1.....(1
CBA
BA
A
Using calculator
>> mode>>
eqn>> unknown
5,4,1 CBA
323
2
2
5
2
4
2
1
2
1
xxxx
x
REPEATED LINEAR FACTOR REPEATED LINEAR FACTOR
22
2
462
xx
xx
222
x
C
x
B
x
A
To find A, B & C
CxBxBxAAxAx
CxxxBxxA
xx
xCxxBxA
244
244
2
22
22
22
2
2
Equal to 2x2+6x-4 AxCBAxBAxx
CxBxBxAAxAxxx
424462
244462
22
222
)3.....(2
)2.......(624
)1.....(44
BA
CBA
A
Using calculator
>> mode>>
eqn>> unknown
4,3,1 CBA
22
2
2
4
2
31
2
462
xxxxx
xx
REPEATED LINEAR FACTOR
32
13
6318
x
xx
22
3
xx
32
11
13
xx
x
QUADRATIC FACTOR (DENOMINATOR)
241
6
xx
x
241 x
CBx
x
A
To find A, B & C
CxCBxBxAxA
xx
xCBxxA
22
2
2
4
41
14
Equal to 6-x CAxCBxBAx
CxCBxBxAxAx
46
46
2
22
)3........(0
)2.......(1
)1.....(64
BA
CB
CA
Using
calculator >>
mode>>
eqn>>
unknown
2,1,1 CBA
22 4
2
1
1
41
6
x
x
xxx
x
QUADRATIC FACTOR (DENOMINATOR)
2435
2152
2
xxx
xx
2435 2
xx
CBx
x
A
To find A, B & C
CCxBxBxAAxAx
xxx
xCBxxxA
55243
2435
5243
22
2
2
Equal to 6-x CAxCBAxBAxx
CCxBxBxAAxAxxx
52543215
55243215
22
222
)3........(252
)2.......(154
)1.....(153
CA
CBA
BA
Using
calculator
>> mode>>
eqn>>
unknown
2,3,4 CBA
243
23
5
4
2435
21522
2
xx
x
xxxx
xx
QUADRATIC FACTOR (DENOMINATOR)
32
232
2
xx
xx
12
42
xxx
x 3624
71872
2
xxx
xx
IMPROPER FRACTION
To find A & B
31
13
3131
75
xx
xBxA
x
B
x
A
xx
x
Equal to 5x-7 BAxBAx
BBxAAxx
375
375
)2......(73
)1.....(5
BA
BA
Using
calculator >>
mode>>
eqn>>
unknown
2,3 BA
3
2
1
31
32
1032
2
xxxx
xx
31
751
xx
x
75
32)(
10332
1
2
22
x
xx
xxxx
32
1032
2
xx
xx
IMPROPER FRACTION
To find A & B
23
32
2323
17
xx
xBxA
x
B
x
A
xx
x
Equal to 7x-1 BAxBAx
BBxAAxx
3217
3217
)2......(132
)1.....(7
BA
BA
Using
calculator >>
mode>>
eqn>>
unknown
3,4 BA
2
3
3
423
6
131332
23
xxx
xx
xxx
23
1723
xx
xx
17
1222)(
1352
1833)(
131336
23
2
2
23
232
x
xx
xx
xxx
xxxxx
x
6
131332
23
xx
xxx
IMPROPER FRACTION
65
311822
2
xx
xx
242
5054322
23
xx
xxx
Workbook Eng. Math BA501, JMSK, PIS
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