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 on $(cx^2+dx+e)^n$

If I have $$\frac{ax+b}{(cx^2+dx+e)^n}$$ with real coefficients and $(cx^2+dx+e)$ has complex roots, what does $$\frac{ax+b}{[c(x-\alpha)(x-\alpha^*)]^n}$$ turn into, in terms of partial fractions?
bobby
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Partial fraction decomposition,how?

I need to decompose this fraction: $${x^2+1\over (x-1)^3\cdot(x+3)}$$ I tried to write it up like this: $${A\over (x-1)}+{B\over (x-1)^2}+{C\over (x-1)^3}+{D\over (x+3)}$$ But now i get $$A\cdot(x-1)^5\cdot (x+3) +B\cdot (x-1)^4\cdot (x+3)…
user128576
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Partial Fraction Using Heaviside cover-up method

How to convert this equation into Partial fraction Using Heaviside Cover-up Method $$\frac{x^2}{(x+2)(2x+3)}$$ After trying to solve this I am ending up getting this which is incorrect : $$-\frac{4}{(x+2)}+\frac{9}{2(2x+3)}$$ Or is there any other…
Abdullah Sorathia
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Quadratic Partial Fraction Decomposition

I am trying to find the inverse laplace transform of $(s^2+4) \over (s-2)(s+2)$. The solution is $ {2\over(s-2)} - {2\over(s+2)} + 1 $. But I can't figure out how to break it up so I can find the solution algebraically. i.e $ (s^2+4)/((s-2)(s+2))…
martinap
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Partial fractions question....

Can someone comment on the following as to whether this partial fractions can be true or not? I'm concerned I've come across a trick question. 1) $\frac{x(x^2+4)}{x^2-4} = \frac{A}{x+2} + \frac{B}{x-2}$ Reason would lead me to believe the answer is…
Wolff
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How to find coefficients in partial fraction?

I have the expression $$\frac{P(s)}{Q(s)}=\left(a_0~\sum\limits_{i=1}^n\frac{c_i}{s+\alpha_i}+1-a_0\right)\frac{B_1(s)}{\prod\limits_{i=1}^m s-\beta_i}$$ where $\alpha_i\neq\beta_i$ are all distinct roots and $deg(B_1(s))
Litun
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Problems solving partial fraction

I have a problem with partial decomposition, I got the next function and should integrate the function so it would be easier to split it in two terms. But I have no idea to start this decomposition due to the unknown a. $\frac{1}{(x+a)(x+1)}$ with…
user2239704
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Partial fraction with complex root with multiplicity >1

I have the function $\frac{x^4}{(x^2+1)^5}$ but I can't remember how to calculate the fractions residues. I know that you can calculate the residues when the root is real and have multiplicity (r) >1 by using $b_{k}$ = $\frac{1}{(r-k)!}$…
Nuno Silveira
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Partial Fraction Decomposition in $ \frac{s^3-1}{(s^2+6)^2(s+12)^2} $.

What special considerations do you need to take when decomposing the following fraction and why? I'm trying to decompose the following: $$ \frac{s^3-1}{(s^2+6)^2(s+12)^2} $$ $$ \frac{s^3-1}{(s^2+6)^2(s+12)^2} = \frac{A}{(s^2+6)^2} +…
Bob Shannon
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Stuck on decomposing partial fraction

I want to decompose the following, and I think got stuck in the thick of it $$ \dfrac{2x^3+3x+1}{(x+1)^2}$$ I tried like this: OK, after advice from @Daniel Fischer and @lab bhattacharjee I decided to use division: first separated the equation as …
Sylvester
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How do I decompose this partial fraction case?

Decompose $$\dfrac{2x}{1+x} $$ Looking at this case, it looks like any simple partial fraction. But it is trickly. This is how I attempted: $$\dfrac{2x}{1+x} = \dfrac{A}{1+x}$$ multiply by LCD $(1+x)$ to get $2x = A$ How to I reduce this to give me…
Sylvester
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Partial Fractions-Hows

I seem to have serious problem understanding entry points of Partial fractions. I would like to decompose the following: $$\dfrac{x^4-8}{x^2+2x}$$. My workings. Please help me judge if I am getting the concept or completely lost: I first simply the…
Sylvester
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Trying to decompose Partial Fraction. Is this the method?

Decompose $\frac{(x^3+x+1)}{(x^2+1)^2}$ Based on my understanding so far: The partials of the denominator are $(x^2+1)$ and $(x^2+1)^2$ $\frac{(x^3+x+1)}{(x^2+1)^2}$ can be decomposed into partial fractions as below: $\frac{(x^3+x+1)}{(x^2+1)^2} =…
Sylvester
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General partial fraction decomposition for a specific type of rational function

Given a rational function of the form $$ \frac{x^k}{(x^n-\lambda_1)(x^m-\lambda_2)}$$ with $k< n+m$, I know we can prove that there are unique polynomials $p(x),q(x)$ with $$ \frac{x^k}{(x^n-\lambda_1)(x^m-\lambda_2)} =…
Will
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Is there a unique partial fraction decomposition for every rational polynomial

Consider this $$({2x-3})/({x^2-1})(2x+3)$$ Here can i do decomposition as $$Ax+B/(x^2-1)+C/(2x+3)$$ Instead of $$A/(x-1)+B/(x+1)+C/(2x+3)$$ And if not then why?
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