All Questions
Tagged with partial-fractions algebra-precalculus
157
questions
2
votes
3
answers
184
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partial fraction question
$ \frac{125x^{2}+x+3}{x^{2}(x-5)} =
> \frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{(x-5)} | * x^{2}(x-5)$
$125x^{2}+x+3 = Ax(x-5) + B(x-5) + C (x^{2})$
$125x^{2}+x+3 = A x^{2} - 5Ax + Bx -5B +Cx^...
- 357
9
votes
4
answers
2k
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Easy ways to find partial fraction representation? (via a concrete example)
In a homework assignment (about generating functions) the students find themselves having to expand $\frac{3-7x+9x^{2}-3x^{3}}{\left(1-x\right)^{4}}$ intro partial fractions. Using some automated tool ...
- 19.4k
7
votes
5
answers
378
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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 ...
- 165
11
votes
6
answers
4k
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The existence of partial fraction decompositions
I'm sure you are all familiar with partial fraction decomposition, but I seem to be having trouble understanding the way it works. If we have a fraction f(x)/[g(x)h(x)], it seems only logical that it ...
- 1,606
9
votes
3
answers
2k
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Partial fraction of $\frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$
How should you break $\displaystyle \frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$ into partial fractions?
- 2,039
39
votes
4
answers
14k
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Integration by partial fractions; how and why does it work?
Could someone take me through the steps of decomposing
$$\frac{2x^2+11x}{x^2+11x+30}$$
into partial fractions?
More generally, how does one use partial fractions to compute integrals
$$\int\frac{P(...
- 1,089
1
vote
2
answers
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How to divide it: $\frac{cx+d}{ax+b}$?
Somebody divided $\frac{cx+d}{ax+b}$ into
$$ \frac{c}{a} + \frac{d- \frac{bc}{a}}{ax+b} .$$ For use for integrals.
Does anybody knows how was it done? Could you show me how to do something like ...
- 217