All Questions
Tagged with partial-fractions algebra-precalculus
157
questions
1
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0
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30
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Partial fractions with a repeated factor [duplicate]
I am looking to find a derivation, or a intuitive explanation as for why a partial fraction with a repeated factor needs to include a factor in the expansion for each power possible. How does one ...
- 845
2
votes
2
answers
245
views
How can i do the following partial decomposition?
I need to prove that:
$$
\frac{1}{(x-a)(x-b)} = \frac{1}{(b-a)(x-b)}- \frac{1}{(b-a)(x-a)},
$$
and I must note that I need to go from the left expression to the right (because of the exercise).
So, I ...
-2
votes
2
answers
109
views
I found an interesting question but I keep getting stuck in a loop. [closed]
Find all values of A, B, C and C such that:
$$
\frac{x-1}{(x-1)(x-2)(x-2)} = \frac{A}{x+1} + \frac{B}{x+2} + \frac{C}{(x-2)^2}
$$
I keep getting into a loop in which:
$$
x - 1 = Ax^2 - 4Ax + 4A + Bx^2 ...
- 15
2
votes
3
answers
83
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Converting a proper fraction into partial fraction
For solving integration-related questions, a rational proper fraction of the form $\frac{px^{2}+qx+r}{(x-a)(x^{2}+bx+c)}$ is decomposed into the sum of the expressions,
$$\frac{A}{x-a} + \frac{Bx+C}{x^...
- 535
1
vote
2
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62
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Contour integral over function $P(x)/Q(x)$: $P(x) = 1$ and $Q(x)$ can be broken into linear factors
a. Let $z_1,z_2,...,z_n$ be distinct complex numbers $(n \geq 2)$. Show that in the partial fractions decomposition
\begin{equation}
\frac{1}{(z-z_1)(z-z_2)\cdots(z-z_n)} = \frac{A_1}{z-z_1}+\frac{A_2}...
- 148
0
votes
3
answers
187
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Partial Fractions Decomposition-Unsure Which Method To Use When
So I was working on this problem and could not use the cover up method to solve it. I was getting the wrong answer.
Find B.
$$\frac{1}{s^2(s^2+4)}=\frac{A}{s}+\frac{B}{s^2}+\frac{Cs+D}{s^2+4}$$
$$s=0: ...
- 53
3
votes
2
answers
222
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Usual method of partial fractions decomposition over the reals seems to fail.
I assumed that it would be straightforward to find the partial fraction decomposition over the reals of the rational function $$f(x) = \frac{1}{(x^2 +1)^2}.$$ However, when I try what I thought would ...
- 188
0
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179
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Question on partial fractions; why numerator has to be one lower degree than denominator?
When decomposing into a partial fraction, why does the highest degree of the numerator have to be one lower than the numerator?
For example:
$\frac{x}{x^3-1} = \frac{a}{x-1} + \frac{bx+c}{x^2+x+1}$
...
- 1,190
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votes
1
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228
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Express in partial fractions and expand the terms using binomial expansion up to $x^3$ [closed]
$$
\frac{2}{(1-x)\left(1+x^{2}\right)}
$$
This is then split into partial fractions
$$
\frac{A}{1-x}+\frac{B x+C}{1+x^{2}}
$$
Computing this i had gotten
\begin{equation}
2=A\left(1+x^{2}\right)+(B x+...
- 161
1
vote
1
answer
124
views
Which integrating technique should I use?
Just some context: In the mathematical course, I have undertaken this year, I've just learnt how to integrate using partial fractions, substitution(not trig though, just a variable) and integrating ...
- 1,190
0
votes
2
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106
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Solution to $\int\frac{\ln(1+x^2)}{x^2}dx$
Q: $\int\frac{\ln(1+x^2)}{x^2}dx$
Here is my entire working:
So, overall, I started with the reverse product rule, then onto reverse chain rule and then tried to partial fraction, however, I still ...
- 1,190
2
votes
4
answers
85
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Finding the partial fractions decomposition of $\frac{9}{(1+2x)(2-x)^2} $
So this is basically my textbook work for my class, where we are practicing algebra with partial fractions.
I understand the basics of decomposition, but I do not understand how to do it when then the ...
- 85
2
votes
5
answers
97
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How to decompose $\frac{1}{(1 + x)(1 - x)^2}$ into partial fractions
Good Day.
I was trying to decompose $$\frac{1}{(1 + x)(1 - x)^2}$$ into partial fractions.
$$\frac{1}{(1 + x)(1 - x)^2} = \frac{A}{1 + x} + \frac{B}{(1 - x)^2}$$
$$1 = A(1 - x)^ 2 + B(1 + x)$$
...
- 1,858
2
votes
0
answers
298
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Are there applications of partial fraction decomposition ( of a rational function) outside integration problems?
I've been recently acquainted with a well known technique called " partial fraction decomposition" which allows, for example to express $\frac {x} {x^2-1}$ as $\frac {1}{2(x+1)} + \frac {1} ...
- 1,796
1
vote
1
answer
388
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Skepticism concerning Heaviside's "Cover-up Method" for partial fraction decomposition
I was reading this paper from MIT and it introduces Heaviside’s Cover-up Method for partial fraction decomposition. In that paper in Example $1$ it solves a problem using that method and just when ...
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