All Questions
10
questions
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 ...
0
votes
1
answer
131
views
Partial Fractions With Repeated Quadratics
I'm told that given a function $f(x)=\frac{P(x)}{Q(x)}$, if $\deg(P)>\deg(Q)$ then $f$ is improper, which makes sense when I think of real numbers like $5/2$. And in this case we would have to do ...
- 2,072
1
vote
1
answer
209
views
Reasoning behind the resolution of partial fractions when denominator is the product of linear factors where some of them are repeating
The following text is from Mathematics for Class XII by Dr. R.D.Sharma, chapter "Indefinite Integrals", topic "Integration of Rational Algebraic Functions by using Partial Fractions&...
- 1,826
0
votes
2
answers
61
views
Integration of rational of polynomials
I want to evaluate the indefinite integral for:
$$
\int\frac{x^3+3x−2}{x^2-3x+2}dx,\quad \text{for } x>2
$$
I did long division and factoring, simplifying it to
$$
\int x+3\,dx + \int\frac{10x-8}{(...
- 115
-1
votes
2
answers
60
views
Equations with 3 unknowns [closed]
I have this equation/problem:
Find the value of A and B
if 2/(x−5)(x+3) = A /(x−5) + B/(x+3)
How can I solve/approach this?
Thank you for your advice.
Regards
Lisa
- 43
0
votes
1
answer
42
views
Why does Partial Fraction Decomposition Result in Multiples of the Decomposed Fraction?
Let's say I have the rational function $\dfrac{x^3}{x^2 + x - 6}$. I use polynomial long division to get $x^3 = (x - 1)(x^2 + x - 6) + 7x -6 \implies \dfrac{x^3}{(x - 2)(x + 3)} = \dfrac{x^3}{x^2 + x -...
- 4,322
7
votes
3
answers
1k
views
Partial fractions and using values not in domain
I'm studying partial fraction decomposition of rational expression. In this video the guy decompose this rational expression:
$$ \frac{3x-8}{x^2-4x-5}$$
this becomes:
$$\frac{3x-8}{(x-5)(x+1)} = \...
- 813
3
votes
1
answer
219
views
Expanding $1/[(s^2+1)(s+1)]$ into partial fractions by brute force
I want to do partial fractions on: $1/[(s^2+1)(s+1)]$
$(as+b)/(s^2+1) + c/(s+1)$
Multiplying both sides by $(s^2+1)(s+1)$, get $a=-1/2, b=1/2, c=1/2$
$(-s/2+1/2)/(s^2+1) + (1/2)/(s+1) = 1/[(s^2+1)(...
- 371
2
votes
2
answers
228
views
problem with partial fraction decomposition
I want to do partial fraction decomposition on the following rational function:
$$\frac{1}{x^2(1+x^2)^3}$$
So I proceed as follows:
$$\begin{align}
\frac{1}{x^2(1+x^2)^3} &= \frac{A}{x} + \frac{...
- 6,276
25
votes
5
answers
5k
views
How does partial fraction decomposition avoid division by zero?
This may be an incredibly stupid question, but why does partial fraction decomposition avoid division by zero? Let me give an example:
$$\frac{3x+2}{x(x+1)}=\frac{A}{x}+\frac{B}{x+1}$$
Multiplying ...
- 25.4k