Question

Resolve into partial fractions 1/[ (x^2 +1 )^2 (x-3) ]

Answer 1

http://answers.yahoo.com/question/index?qid=20100811085245AAwrqXD
look @ this @Yahoo! :)

Answer 2

Is it :

\[1 = \frac{Ax + D}{(x^2 + 1)} + \frac{Bx + E}{(x^2 + 1)^2} + \frac{C}{(x-3)}\]
I am not sure..

Answer 3

yes it is !!!

Answer 4

@lgbasallote help here..

Answer 5

do this works @Yahoo! ?????

Answer 6

If it right then half of our work is finished..

Answer 7

No.

Answer 8

you can check it here your decomposition is correct !
http://www.wolframalpha.com/input/?i=Partial+fractions1%2F%5B+%28x%5E2+%2B1+%29%5E2+%28x-3%29+%5D

Answer 9

Sorry there will come denominator also..

Answer 10

No matters..

They will cancel out after taking LCM..

Answer 11

Now let us find A, B , C D and E..

Answer 12

@waterineyes i have the answer key

Answer 13

Keep it with yourself..

Answer 14

i think u r correct plzz procede

Answer 15

After taking LCM we get:

\[1 = (Ax + D)(x^2 + 1)(x-3) + (Bx +E)(x^2 + 1)(x-3) + C(x^2 + 1)^2\]

Answer 16

now compare coefficients..:

firstly for \(x^4\)..

A + B + C = 0

Put x = 3:

C(10) = 1

C = 1/10

Answer 17

*100.

Answer 18

\[C = \frac{1}{100}\]

Answer 19

Sorry I have done wrong..

Answer 20

\[1 = (Ax + D)(x^2 + 1)(x-3) + (Bx +E)(x-3) + C(x^2 + 1)^2\]

Answer 21

From here when putting x = 3 we get:

\[C =\frac{1}{100}\]

Answer 22

Compare the coefficients of \(x^4 \) here:

A + C = 0

From here:

\[A = \frac{-1}{100}\]

Answer 23

Sorry:

\[D = \frac{-3}{10}\]

Answer 24

Now you have to find B..

Answer 25

Yes I am..

Answer 26

Have to do once again..

A C and D is right..

Answer 27

B and E must be checked once again..

Answer 28

No D is not right..

Answer 29

Yeah I got for D..

Check the coefficient of \(x^3\) there :

\[-3A + D = 0\]
\[D = 3A \implies D = \frac{-3}{100}\]

Answer 30

Now we got A, C and D..

Answer 31

Compare the constant terms here:

\[-3D -3E + C = 1 \implies -3E = 1- \frac{1}{100} - \frac{9}{100} \implies \frac{90}{100} \implies E = \frac{-3}{10}\]

Answer 32

Compare the coefficients of \(x\) here:

\[-3A + D - 3B + E = 0\]

\[3B = \frac{3}{100} - \frac{3}{100} - \frac{3}{10} \implies 3B = \frac{-3}{10} \implies B = \frac{-1}{10}\]

Answer 33

So you have all the values now:

\[A = -\frac{1}{100}, D = -\frac{3}{100}, B = - \frac{1}{10}, E = -\frac{3}{10} \; and \; C = \frac{1}{100}\]

Answer 34

So now you can rearrange your expression to:

\[\implies \color{blue}{\frac{-x -3}{100(x^2 + 1)} + \frac{-x -3}{10(x^2 + 1)^2} + \frac{1}{100(x-3)}}\]

Getting @Yahoo!

Answer 35

Yup .... thxx

Answer 36

Welcome dear..