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.

1254 questions
0
votes
0 answers

Proof of partial fraction decomposition without using complex numbers and properties of complex field

Does somebody know the proof of partial fraction decomposition theorem for rational functions over field of real numbers that does not use properties of field of complex numbers?
someone
  • 1
0
votes
2 answers

Having Trouble Decomposing This Partial Fraction

1/(s^2)((s-3)^2) I'm having trouble decomposing this particular fraction. Wolfram won't help, and other forums only suggest to use a CAS program.
Eduardo Montes
  • 1
0
votes
1 answer

Restrictions for using partial fractions

When given a fraction with both numerator and denominator as polynomials, and where the denominator is expressed as a multiplication of factors. Can we always use the partial fractions method for splitting the overall fraction into several…
Andrew Brick
  • 1,296
0
votes
1 answer

A problem about partial fraction

I met a strange problem about partial fraction. It asks me to find the partial fraction of $\frac{(s+1)(s+2)(s+3)}{s(s^2+s+1)}$. I know I should use $s^2+s +\frac{1}{4}$, but what to do next? Thanks
Bote
  • 1
0
votes
0 answers

Why long division for partial fractions with numerator of equal degree as the denominator?

$\frac{x^2+3}{(x+5)(x+6)}=1-\frac{11x+27}{(x+5)(x+6)}$ If you substitute $x$ with any ordinary value like $2$, you will find that value of the numerator is lower than the denominator's. So why do we still have to perform long division to get partial…
brillydev
  • 11
0
votes
0 answers

Show that every infinite recursive set is the range of a nondecreasing unbounded recursive function of one variable.

I came across this problem and I was not able to solve it: Show that every infinite recursive set is the range of a nondecreasing unbounded recursive function of one variable. Also, what would be the case if the function is bounded? Thanks :)
Salma
  • 97
0
votes
3 answers

How to come from $\frac{z^{2}}{z^{2}+1}$ to $\frac{z/2}{z+i}+\frac{z/2}{z-i}$

As title says, how to come from $\frac{z^{2}}{z^{2}+1}$ to $\frac{z/2}{z+i}+\frac{z/2}{z-i}$? Here is what I did: $\frac{z^{2}}{z^{2}+1}=1-\frac{1}{z^{2}+1}=1-\frac{1}{(z-i)(z+i)}$
Igor
  • 13
0
votes
0 answers

How do we know the form of a partial fraction expansion?

If you take a quick gander at the table on this page: http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx You'll notice there are some rules about what the form of a partial fraction expansion should be, based on the factors of the…
Mahkoe
  • 364
0
votes
1 answer

Why Bx+C for irreducible quadratic but not perfect square? (Partial fractions)

When you partial fraction something like $$\frac{x+2}{(x+3)(x+2)^2}$$ you make it $$\frac{a}{(x+3)}+\frac{b}{x+2} + \frac{c}{(x+2)^2}$$ but when you have $$\frac{10x^2+12x+20}{(x-2)(x^2+2x+4)}$$ you make it…
dngr193
  • 169
0
votes
1 answer

Find partial fractions of $\frac{x^2-1}{x^4+1}$

I tried to figure out how WA found the partial fractions of $\frac{x^2-1}{x^4+1}$: Help is Appreciated.
Mohamed Mostafa
  • 1,228
0
votes
2 answers

Partial Fraction confusion

How to solve this using partial fraction $$\frac{x^2+7}{(2x-1)(x-1)}$$ I am using $\frac{A}{2x-1}+\frac{B}{x-1}$ but not getting it
Milan Amrut Joshi
  • 1,109
0
votes
2 answers

Repeated Root Partial Fraction Decomposition: Derivative Aproach

I am trying to solve for H1, I was able to get the Coefficients for B,C, and D. Yet, I have forgotten how to solve for A. All I can remember is that one must take the derivative of both sides. After that, I can not remember and I rather not use a…
James Hayek
  • 103
0
votes
2 answers

Partial Fraction for $x^2/(x^2 +1)^2$

$$\begin{aligned} \frac{\ x^2}{(x^2+1)^2} \\ \ \end{aligned}$$ I am new to partial fractions and this is what I have so far: $$\begin{aligned} \dfrac{(x^2)}{(x+1)^2} = \dfrac A{x-1}+\dfrac B{(x+1)^2} \ …
jake mckenzie
  • 343
0
votes
1 answer

Partial fractions, proper fraction with a perfect square factor

I think I have figured why the following is the case, I need however a confirmation that it is indeed so. Consider: $\displaystyle{\frac{x-1}{(x+1)(x-2)^2} \equiv \frac{A}{x+1} + \frac{Bx+C}{(x-2)^2}} \ \ (i)$ Now the book is showing the following…
Naz
  • 3,289
0
votes
2 answers

Complex partial fraction

Good day! I'm currently having an exercise on partial fractions... I know the basic of different methods in separating a fraction into smaller parts but I got confused when I encountered this one$$\frac {(n + 1)^2 (t^{2n})}{(t^{2n+2} - 1)^{2}}$$ is…
rosa
  • 1,171
1 2 3
…
13
14