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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