Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [partial-fractions]

Rewriting rational function in the form of partial fractions is often useful when calculating integrals.

Rewriting rational function in the form of partial fractions is often useful when calculating integrals. The possibility of decomposing a rational function into a sum of simplified fractions is guaranteed by the fundamental theorem of algebra.

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Partial Fractions with Quadratic Factor

I understand that if we have a quadratic factor such as in $\frac{8}{(x^2 + 1)(2x-3)} $ and we want to decompose, we should have a linear factor above $ x^2 +1$. Is the reason behind this primarily for calculus purposes, since if we have the…
user342258
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Proving $A_1, A_2, \dotsc, A_k$ are real numbers in an arbitrary partial fraction decomposition.

I have two extra credit assignments for my Calculus 2 class and after attempting them for several days and unsuccessfully trying to find any resources on how to do these questions I've decided to ask here. The first question is as follows: Let…
user276019
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Trouble with partial fractions and complex numbers

$$f(z) = \frac{3}{(z+1)(z-i)} = \frac{A}{z+1} + \frac{B}{z-i}$$ $$z(A + B) + B - Ai = 3$$ $$A + B = 0$$ $$B-Ai=3$$ Somehow, I end up with $B = - \frac{3}{(1+i)}$ Is that the way to go?
paranoidhominid
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Partial fractions problem help

I need help with the following: $\frac{1}{(x-1)^2(x+1)}$ Using the "cover-up" method, I can identify the numerator of the fraction with the denominator $(x+1)$ fairly quickly, and it is $1/4$. Then I arrive at the following: $$1 \equiv (1/4)(x-1)^2…
Naz
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Partial fraction of $\frac 1{x^6+1}$

Can someone please help me find the partial fraction of $$1\over{x^6+1}$$ ? I know the general method of how to find the partial fraction of functions but this seems a special case to me..
Wanderer
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Partial Fractions and L'Hopital's Theorem

I've been reading about partial fraction expansions using L'Hopital's Theorem and have found this document. I was wondering if it were possible to use the method mentioned in the link to find all the coefficients of a function with a perfect square…
user968243
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Partial fraction question with squared

How could one apply partial fraction decomposition to $$\left(\frac{s}{s^2+4}\right)^2$$ I tried to separate by doing $$\frac{A}{s^2+4} + \frac{B}{s^2+4}$$ and I got strange solution $A+B=0$ and $A+B=1$.
dsaca
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Expanding $\frac{1}{z^3-z}$

How would I use partial fractions to expand the following equation? $\frac{1}{z^3-z}$ I have tried changing re-writing that as: $\frac{1}{z(z-1)(z+1)}$ But I have a problem finding the numerators of the fraction when written…
Amir Omidi
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Partial Fraction Decomposition Clarification

I'm just looking for some overall clarification for the following cases. Now, to the extent of my knowledge, the following examples of partial fractions would be split up in the following…
bjd2385
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integration using partial fraction with repeating denominator

So i need to integrate this $1/[(x^3)(x-1)]$, that means it could be decomposed into: $$A/x + B/x^2 + C/x^3 + D(x-1)$$ Furthermore the resulting equation would then be: $1 = A(x^2)(x-1) + Bx(x-1) + C(x-1) + Dx^3$ if i let $x=0$ then $C=-1$ if i let…
sheila
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partial fraction problem

I have thought for a long time but general method is not working : $$\frac{s^2+2}{(s+2)^2(s^2+2s+2)^2}$$ Thanks for all help.
Viduino
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Partial fraction of $\frac{2x^2-9x-9}{x^3-9x}$

I'm doing some questions from Anton, 8th edition, page 543, question 13. I've found a answer but it does not match with the answer given at the last pages. Questions asks to solve…
Fabiano Araujo
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How do I partial fraction this

I have this fraction that I want to express as partial fractions: $$\frac{s}{(s^2+1)(s-1)}$$ How do I do it? I came as far as the expression: $$s=A(s-1)+B(s^2+1)$$ But how do I solve this for A and B?
rablentain
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integrating method (maybe PFD)

I am trying to integrate: dt = 1/(ax-bx^2) * dx I am guessing I need to use Partial Fraction decomposition, can someone help show me how to begin this process?
Jackson Hart
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Starting a Partial Fractions Question

I have the question $$ \frac{ 3x + 3 }{ (x-1)(x^2 +x +1) } $$ and I am unsure about how to start as the quadratic on the denominator is irreducible. So anyone got any tips for starting this one?
Abby
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