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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Can someone run me through using heaviside cover-up for this decomposition

Can someone run me through using Heaviside cover-up for this decomposition: $$ \frac{2}{(x-2)(x+3)(x+1)^3} $$ I have calculated the decomposition traditionally but can't get consistent answers using Heaviside. Any help appreciated :) edit: I…
trawling
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Question about partial fractions with repeated linear factors

I am teaching A Level Maths, and have a question about partial fractions. When there is a denominator with a repeated linear factor, such as the following example: $$\frac{2x+9}{(x-5)(x+3)^2}$$ the exercise book, and all similar examples, say that…
harpomiel
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Partial Fraction Expansion Algebra Help

I hope someone can help. Given this equation $$ F(s) = \frac{(1 - e^{-x})s^{-1}}{(1 - s^{-1})(1 - e^{-x}s^{-1})} $$ Apply a PFE $$ = \frac{A_{1}}{1 - s^{-1}} + \frac{A_{2}}{1 - e^{-x}s^{-1}} $$ Then $$A_{1} = 1$$ $$A_{2} = -1$$ And $$ F(s) =…
user1011182
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Wy can a fraction with $(x+\alpha)^n$ in the denominator be partially decomposed into n different fractions?

My textbook in algebra states without proof that: A rational function: $$s(x)=\frac{p(x)}{(x-\alpha)^m(x-\beta)^n}$$ Where $\alpha \neq \beta$ and $\deg(p(x)<\deg(m+n)$, can always be partially decomposed…
Magnus
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How to solve Partial Fraction- Improper Fractions

Kindly can someone please help me solve this particular question from the start till the end. I don't know how to solve partial fractions with improper fractions. Please show me step-by-step working to…
Sugi
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Coefficients for partial fraction decomposition

I'm not sure if this question has been asked somewhere but I couldn't find an answer to it. I need the coefficients in this partial fraction decomposition but in a specific way:$$\frac{1}{(x^2-b^2)^n}$$I know that it can decompose…
MoonTurtle
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How to separate the following fraction into partial fractions?

I have that $$\frac{x^2(1-x)}{(1-x)^3} = \frac{x^2}{(1-x)^3} -\frac{x^3}{(1-x)^3} $$ Assuming we begin by cancelling the $(1-x)$ on top with one of those on the bottom, how do we go about splitting $\dfrac{x^2}{(1-x)^{2}}$ into the two partial…
rainingagain
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Partial fraction with complex roots

Is it so that partial fractions with complex roots can work sometime, and sometime not? I have tried to check a result by WA here, and tried to solve it…
Luthier415Hz
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Partial Fractions with Two Repeated Linear Terms

Rewrite the expression below into partial fractions $$\frac{\omega s}{(s+\omega)^2(s-\omega)^2}$$ I started by taking the general form $$\frac{A}{(s+\omega)} + \frac{B}{(s+\omega)^2} + \frac{C}{(s-\omega)} + \frac{D}{(s-\omega)^2}$$ Then, using the…
Iuri
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Partial fraction decomposition trouble with a problem

I have this integral: $$ \int \frac{1}{(1+x^2)(1+(z-x)^2)} {\rm d}x $$ and I want to perform partial fraction decomposition in this form $$ \int \left( \frac{Ax + B}{1+x^2} + \frac{Cx + D }{1+(z-x)^2} \right) {\rm d}x $$ but I can't get the right…
Raffer Flameline
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Partial Fraction Decomposition (Complex Numbers)

I'm going insane with this question from a previous exam: How do I get the partial fraction decomposition of: $${15 \over (z-3i)(2z-3)}$$ I don't understand how to 'equate' anything here. If we have that $$15=a(2z-3)+b(z-3i)$$ then how am I meant to…
ThunderHex
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Calculate partial fractions

calculate partial fractions for: $1/x^2(x^2 + 1)$ I have tried solving by expanding it like this: $A/x^2 + B/ (x^2 + 1)$ and it results in the right answer as given in class. But partial fractions expansion rules suggest that I have to expand it…
siddharth tanwar
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Aren't the signs of coefficients $ A _ 1 $ and $ A _ 2 $ to be interchanged in this partial fraction method?

Consider the following partial fraction expansion: $$ H ( s ) = \sum _ { k = 1 } ^ 2 \frac { A _ k } { s - p _ k } = \frac { A _ 1 } { s - p _ 1 } + \frac { A _ 2 } { s - p _ 2 } $$ $$ \frac { 0.264 } { s ^ 2 + 0.513 s + 0.33 } = \frac { A _ 1 } { s…
abdulkhan
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Are you supposed to perform partial fraction decomposition for a quadratic component that factorizes to rational numbers?

Let's say you have to spread a cubic equation into partial fractions. What you would normally get is a linear factor and a quadratic or a linear and 2 linear expressions. My question is, for that quadratic factor ,if the solutions are fractions (for…
sweet lovely
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Reason behind partial fraction decomposition for a quadratic factor

Can we use either $$ \frac{x-5}{(x-2)^2 (x+1)} = \frac{A}{(x-2)^2} + \frac{B}{(x-2)} + \frac{C}{(x+1)} $$ or equivalently, $$ \frac{x-5}{(x-2)^2 (x+1)} = \frac{A'x+B'}{(x-2)^2} + \frac{C}{(x+1)} $$ since $(x-2)^2$ is a quadratic factor. My teacher…
I'm a lightbulb
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