All Questions
Tagged with partial-fractions algebra-precalculus
157
questions
1
vote
0
answers
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 ...
- 855
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 ...
- 11.2k
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,
$$\frac{A}{x-a} + \frac{Bx+C}{x^...
- 9,692
-2
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2
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109
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I found an interesting question but I keep getting stuck in a loop. [closed]
Find all values of A, B, C and C such that:
$$
\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 ...
- 25.2k
18
votes
9
answers
8k
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Derivation of the general forms of partial fractions
I'm learning about partial fractions, and I've been told of 3 types or "forms" that they can take
(1) If the denominator of the fraction has linear factors:
$${5 \over {(x - 2)(x + 3)}} \equiv {A \...
- 156
25
votes
5
answers
5k
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How does partial fraction decomposition avoid division by zero?
This may be an incredibly stupid question, but why does partial fraction decomposition avoid division by zero? Let me give an example:
$$\frac{3x+2}{x(x+1)}=\frac{A}{x}+\frac{B}{x+1}$$
Multiplying ...
- 275k
3
votes
4
answers
4k
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Partial Fractions with a Repeated and a Irreducible Quadratic factor
I am trying to make this into a partial fractions form but i can't seem to find a way to do it.
The question is here:
Change into a partial fractions form.
\begin{align}
\frac{2s}{(s+1)^2(s^2 + 1)}...
- 275k
1
vote
3
answers
216
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Partial fraction decomposition of $\frac{x-4}{(x-2)(x-3)}$
I'm trying to do the partial fraction decomposition of the following rational expression:$$\frac{x-4}{(x-2)(x-3)}$$
Here are the steps I preformed:
\begin{align*}
x-4 & = \frac{A}{x-3} + \frac{B}{...
- 740
2
votes
1
answer
431
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How to expand $\frac{5}{(x+1)(x^2-1)}$ into partial fractions
I know how to do these problems, but this one is giving me some trouble:
Expand the following into partial fractions$$\frac{5}{(x+1)(x^2-1)}$$
Should I break it down into:
$$\frac A{x+1}+\frac B{x-1}...
- 740
2
votes
1
answer
187
views
Finding the partial sum of the series $\sum_{n=1}^{\infty}\frac{n}{n^4+n^2+1}$
Hi asked the following question yesterday: Obtaining the sum of a series
Given the answers to that question by wj32, I am now trying to solve the following problem:
Consider the series
$$\sum_{n=1}^{...
- 740
7
votes
5
answers
378
views
Evaluate $\int{\frac{4x}{(x^2-1)(x-1)}dx}$
So I know I need to use the partial fractions method to solve this integral. However when I split it as:
$$\frac{4x}{(x^2-1)(x-1)} = \frac{Ax + B}{x^2-1} + \frac{C}{x-1}$$
I find that I can't solve ...
- 20.6k
1
vote
2
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62
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Contour integral over function $P(x)/Q(x)$: $P(x) = 1$ and $Q(x)$ can be broken into linear factors
a. Let $z_1,z_2,...,z_n$ be distinct complex numbers $(n \geq 2)$. Show that in the partial fractions decomposition
\begin{equation}
\frac{1}{(z-z_1)(z-z_2)\cdots(z-z_n)} = \frac{A_1}{z-z_1}+\frac{A_2}...
- 102k
7
votes
2
answers
2k
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Integration of high order fraction; explanation of method.
I understand the cases where the order is less or equal to 3 (example where it is three we split numerator with A,B,C), but in this case(Example 8) I do not see why we split the numerator with A, Bx+C,...
- 102k
0
votes
2
answers
179
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Finding nth derivative of $\frac{1}{x^4+4}$
I am supposed to find the nth order derivative of:
$$\frac{1}{x^4+4}$$
I tried to resolve into partial fractions. But it didn't work out for me.
Edit- where I am stuck
$$\frac{1}{x^4+4}=\frac{1}{(x-1+...
- 1,846
0
votes
3
answers
190
views
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: ...
- 33.9k