Need help with partial fractions integral question (1 Viewer)

[Zorren]

Hey guys,

I'm looking for a little bit of assistance with a question. Any help would be really appreciated! Its question 1D. Thanks in advance

 

[integral95]

it needs to be in the form




times both sides by (x-1)^2(x+1)^2 and equate coefficient.

So you start by getting



Sub in x = -1 and x = 1 (seperately) to get B and D respectively

Equate X^3 coefficient to get A+C = 0

equate constants to get -A+B+C+D = 4

and use simult equation to find A and C (that's after you found B and D of course)

 

[Zorren]

Thank you very much for your response I understand your working. But may I ask why did split the fraction into 4 components rather than 2 at the start?

 

[integral95]

Hmm I don't remember the reason behind that tbh

might need to ask someone else this (anyone?? )

 

[Zorren]

Thanks anyway dude

 

[seanieg89]

Thank you very much for your response I understand your working. But may I ask why did split the fraction into 4 components rather than 2 at the start?

Whenever there are factors with multiplicity > 1 in the denominator you will need to do this.

 

[Zorren]

Yeah I've just worked it out, you have to square the denominators to get up with the same denominator of the original fraction

 

[Kurosaki]

Hmm I don't remember the reason behind that tbh

might need to ask someone else this (anyone?? )

, and you decompose these again.