Partial Fractions: Deciding Formula Without Memorization

[pivoxa15]

I have never remebered the different partial fraction forumlas. Is there a way to decide which partial fraction formula to use just by looking at the expression?

 

[Office_Shredder]

Partial fraction formulae?

I thought you just did partial fractions... what's the context? Normally you just split the fraction after factoring the denominator into a sum of fractions with denominators equal to the different factored parts

 

[mathwonk]

over R, the only prime polynomials are linear or quadratic. the numerators are either constant or linear respectively.

if f^n is a factor of the denominator, where f is prime, we need to allow for all fractions whose greatest common denom is f^r, so we have

to allow a/f , b/f^2, c/f^3, ..., d/f^n, for appropriate numerators.

e.g. to decom,pose h/[x^2(x^2+x+1)^3] we set it equal to

a/x + b/x^2 + (cx+d)/(x^2+x+1) +(ex+f)/(x^2+x+1)^2 + (gx+h)/(x^2+x+1)^3.where a,b,c,d,e,f,g,h, are constants.

 

[pivoxa15]

over R, the only prime polynomials are linear or quadratic. the numerators are either constant or linear respectively.

if f^n is a factor of the denominator, where f is prime, we need to allow for all fractions whose greatest common denom is f^r, so we have

to allow a/f , b/f^2, c/f^3, ..., d/f^n, for appropriate numerators.

e.g. to decom,pose h/[x^2(x^2+x+1)^3] we set it equal to

a/x + b/x^2 + (cx+d)/(x^2+x+1) +(ex+f)/(x^2+x+1)^2 + (gx+h)/(x^2+x+1)^3.


where a,b,c,d,e,f,g,h, are constants.

Is that all there is to partial fractions? It isn't as mystifying as it appears.

 

[arildno]

Is that all there is to partial fractions?

Yes it is!

It isn't as mystifying as it appears.

No, it isn't!