Find the form of the partial fraction decomposition of the following rational function.
((x-1)(x+5)(x^2+17)^2)/ (x^3(x+1)^2(x^2+8))

Question

Find the form of the partial fraction decomposition of the following rational function.  
((x-1)(x+5)(x^2+17)^2)/ (x^3(x+1)^2(x^2+8))

hartnn · Answer

where exactly are u stuck ??

anonymous · Answer

I don't know where to start

hartnn · Answer

this is very lengthy
u have solved any partial fractions problem earlier ?

anonymous · Answer

no this is the first one, and its due within an hour :(

hartnn · Answer

do u have options ?

anonymous · Answer

what do you mean?

anonymous · Answer

it says i do not have to determine the values for a 1 or a 2

hartnn · Answer

choices ... something to choose from.

hartnn · Answer

where does a1 or a2 come from ?

anonymous · Answer

Find the form of the partial fraction decomposition of the following rational function. You do
NOT need to determine the values of the constants A1,A2, . . . (or A,B, . . .).

anonymous · Answer

that is the entire question

hartnn · Answer

okk, then its not much lengthy
u have denominator as

hartnn · Answer

$x^3(x+1)^2(x^2+8)$ 
right ?

anonymous · Answer

yes that is denominator

hartnn · Answer

if only x^3
then u write $A1/x+A2/x^2+A3/x$
ok ?

anonymous · Answer

ok, where should i write that at

hartnn · Answer

wait, for (x+1)^2
u have $A4/(x+1)^2+A5/(x+1)$
and for x^2+8
u have $\frac{A6x+A7}{x^2+8}$
now just add all of them...

anonymous · Answer

so what would it look like in the end?

hartnn · Answer

$\huge\frac{A_1}{x}+\frac{A_2}{x^2}+\frac{A_3}{x^3}+\frac{A_4}{(x+1)^2}+\frac{A_5}{x+1}+\frac{A_6x+A_7}{x^2+8}$

anonymous · Answer

is this the work?

hartnn · Answer

yup. your final answer.

anonymous · Answer

but how can it be that easy though, all you did was just spread out the values????

hartnn · Answer

its easy because you don't have to find the values of constants, just know how to decompose

anonymous · Answer

so it was just a one step process then?

hartnn · Answer

yes, if u need to show work, show it separately for each denominator , then add.

anonymous · Answer

can you just show me an example for the first term then on how to do that?

hartnn · Answer

like how to find values of constants ??

anonymous · Answer

the showing the work part

hartnn · Answer

see my 1st comment after your comment 'yes that is denominator'
thats where i have shown it, in one line....A1/..........

anonymous · Answer

thanks man

hartnn · Answer

welcome :)