Partial fractions Definition and 298 Threads

Homework Statement I don't understand something I have read about partial fractions so I wonder if anyone can help! To each repeated linear factor in the denominator of the form (x-a)^2, there correspond partial fractions of the form : A/(x-a) + B/(x-a)^2 Is this true if we have...

I don't fully understand the logic of this example: For, 4x^2-3x+5/(x-1)^2(x+2) we need: A/(x-1)^2+B/(x-1)+C/(x+2) It is also correct to write Ax+B/(x-1)^2 + C/(x+2) but the fractions are not then reduced to the simplest form. How do the 2nd fractions simplify to give the 1st set of...

It says in my book that a any function can be decomposed to some sum of strictly proper rational functions where the denominator of each rational function is either consist of linear functions, irreducible quadratic functions. "Any proper rational function can be expressed as a sum of...

Need a check on the last problem of my test: integral (3x^2-8x+13)/(x^3+x^2-5x+3) Factor for the denom is (x-1)(x-1)(x+3). So a/(x-1) + b/(x-1)^2 + c/(x+3) = the f(x) in the integral Factor out and multiply all the polynomials. Comes down to a = -1, b = -2, c = 2 Integral...

Im going to Durham uni in oct to do physics, and the nice people of the physics department sent me some maths questions to do before I arrive. One of the partial fractions questions looked simple enough, but when I did it, I got it wrong...so with the answer they give, i worked back to the...

f(x) is a polynomial. A product of n distinct factors (x-a_{i}). Prove that \frac{1}{f(x)}=\sum\frac{1}{f'(a_{i})}.\frac{1}{(x-a_{i})} This I can do by writing f(x)=(x-a)g(x) where g(a)<>0. Then splitting \frac{1}{f(x)} into \frac{A}{(x-a)}+\frac{h(x)}{g(x)} for some...

Homework Statement [(3x^2)+10x+13]/[(x-1)([x^2]+4x+8)] Homework Equations I think solving this question should include partial fractions. The Attempt at a Solution I've made a few different attempts at this question but find myself at a dead end every time. One attempt was...

Homework Statement I just want to know how to proceed to get 1/s - s/(s^2+1) using partial fractions on the term 1/(s(s^2 − 1)) I know this is probably straight forward but I just don't get it. Thanks.

The problem is \int \frac{2s+2}{(s^2+1)(s-1)^3} dx What I'm wondering about is there anyway to get the partial fractions out without doing the full mess of bringing up the (s^2+1) and (s-1)^3 ? I tried the heaviside method and got one of the numerators but I'm stuck for a practical way to do...

Homework Statement the question can be ignored - it involves laplace and Z transforms of RLC ckts. Vc(s) = 0.2 ----------------- s^2 + 0.2s + 1 find the partial fraction equivalent such that it is : -j(0.1005) + j (0.1005) --------------...

if you have \frac{3s + 1}{(s+2)^2 + 4^2} does it become... 3s + 1 = \frac{A}{(s+2)} + \frac{B}{(s+2)^2} + \frac{C}{4} + \frac{D}{4^2} or... 3s + 1 = \frac{A}{(s+2)} + \frac{B}{(s+2)^2} + \frac{C}{4^2}

Homework Statement integrate((x^3+72)/(x^2+6x+8))dx Homework Equations The Attempt at a Solution I decided to use partial fractions method. x^2+6x+8 factors to (x+4)(x+2) x^3+72=A(x+2)+B(x+4) when A=-2, 64=B(2), B=32 when B=-4, 8=A(-2), A=-4 -4*int(1/(x+4)) +...

Homework Statement I need to integrate this differential equation using partial fractions to obtain an equation for P in terms of t; P(t): 1/P dP/dt = b + aP Homework Equations The Attempt at a Solution So far, this is what I have: ln /P/ = bP + aP^2/2 +c...

I have: \frac{(1+j\omega)(3-j\omega)}{(3+j\omega)(3-j\omega)} When I perform the partial fraction expansion I get: \frac{-2}{3+j\omega} Where my calculator gets: 1 - \frac{-2}{3+j\omega} . Why am I wrong? I am performing the expansion as follows: \bar F(s) =...

Homework Statement Suppose that a town has a population of 100,000 people. One day it is discovered that 1200 people have a highly contagious disease. At that time the disease is spreading at a rate of 472 new infections per day. Let N(t) be the number of people (in thousands) infected on...

Hi Guys, can anyone help with this problem? resolve 3 -x ---------------- (x^2 +3) (x + 3) The problem I have is with the x^2, when substituting numbers for x at the end to find A and B. I can only use -3

dumb partial fractions question... suppose i get x+1=A(x-2)+B(x-2) how do you then find A and B?

Given that \frac{dx}{dt} = k(a-x)(b-x) : (a) Assuming a \neq b , find x as a function of t . Use the fact that the initial concentration of C is 0. (b) Find x(t) assuming that a = b . How does this expression for x(t) simplify if it is known that [C] = \frac{a}{2} after 20...

stuck on this one question. mostly cause I don't know the proper steps for using partial fractions. (4x-4)/(x^4 -2x^3 +4x^2 -6x +3) which factors to (4x-4)/(x^2+3)(x-1)^2 now I have the answer here. but I don't know the rules for decomposing this fraction. can someone go over them for me...

Hi, IM trying to evaluate this, and I can't get started..I tried integration by partial fractions and substitution but I keep getting stuck. \int_0^2 \frac{x-3}{2x-3}dx Any hints would help, Thanks

http://album6.snapandshare.com/3936/45466/776941.jpg PS. Just wanted to say thanks for all the help so far. This is a really great forum and I am receiving tons of help. I like how people here are not just blurting the answers, but are actually feeding me ideas so that I may work them out...

Hi, I'm having quite a bit of trouble with this topic. Here's one of the first problems, I don't really understand the method in the book, if someone could show me an easy route, it would help. \int_{0}^{1} \frac {2x+3}{(x+1)^2}dx Thanks

I'm supposed to integrate this using partial fractions: \int\frac{1}{(x-1)^2(x+1)} \ dx I've started to split the integrand into more readily integrated fractions by stating... \frac{A}{(x-1)}+\frac{B}{(x-1)^2}+\frac{C}{(x+1)} = \frac{1}{(x-1)^2(x+1)} combining the fractions via addition...

I need to find the following intergral: \int_{0}^{1} \frac{28x^2}{(2x+1)(3-x)} \;\; dx So I split it into partial fractions thus: \frac{2}{2x+1} + \frac{36}{3-x} - 14 Then integrated: \int_{0}^{1} \frac{2}{2x+1} + \frac{36}{3-x} - 14 \;\; dx = \left[ \ln\left| 2x+1 \right| +...

I really find in difficult to solve the second part of these type of questions, Here are two questions of them Question number 1 Resolve into partial fractions 1+x/(1+2x)^2(1-x) For what range of values of "x" can this function be expanded as a series in ascending powers of "x"...

Hey guys, I am supposed to find the Laplace transform of a set of ODEs. Ive broken it down a bit and I am left with finding the Laplace transform of: (-2e^-s)/(s(s+4)(s+1)) Is this something I have to use partial fractions for? Or is there another way? I am a bit confused.

This next problem is rather strange and it once again involves quadratic factors and I am not able to get the correct answer. The problem is: \int \frac{7x^3-3x^2+73x+53}{(x-1)^2(x^2+25)}dx Step I: 7x^3-3x^2+73x+53 = A(x-1)(x^2+25)+B(x^2+25)+(Cx+D)(x-1)^2 I easily get the value of B by...

I started this section off quite well and I did very well on the problems where there are only linear factors but when I got to the problems with quadratic factors, I began getting wrong answers. I though that perhaps I would receive some advice or my error/mistake could be corrected if...

\int \frac{x^2 + 2x}{x^3 + 3x^2 + 4} dx I can solve it directly by using substitution . But how to solve it by using partial fraction? Is it possible?

So, what I'm going to do in this thread is show a general method for finding the antiderivative (ie, indefinite integral) of any rational function. Here, a rational function is a function of the form P(x)/Q(x), where P(x) and Q(x) are polynomials, and the antiderivative of a function f(x) is...

How does this work? All i really understood from class was that you would factor the integrand and then somehow A and B were involved, and you would use systems of equations to find A and B. What's the middle ground? Thanks in advance!:biggrin:

Partial Fractions: A single infected individual enters a comunnity of n susceptible individuals. Let x be the number of newly infected individuals at time t. The common epidemic model assumes that the disease spreads at a rate proportional to the product of the total number infected and the...

Ok... I'm working on this laplace transform, and I'm getting stuck on the partial fractions part on this one problem. If someone could help me out with setting it up, I would be very appreciative. \frac{s}{(s^2+4)(s^2+\omega^2 ) } After trying to set it up, I get something like...

\int \frac {1}{x\sqrt{4x+1}}dx Here's what I have done so far on this problem I let u= \sqrt{4x+1} , so then u^2=4x+1 , du= \frac {2dx}{u} and x= \frac {u^2-1}{4} Substituting, I get \int \frac {1}{(\frac{u^2-1}{4})u}du Then moving stuff around, I get 4 \int \frac...

(5x^4-6x^3+31x^2-46x-20)/(2x^5-3x^4+10x^3-14x^2+5) I got it = 1/(2x+1) + 4.75/(x-1) + -2/(x-1)^2 + 8.75(x^2+5) My working was several pages so I am not going to post it. I was wondering if any of you know if that is right? Are there any geniuses on here who can do them in there head?

Hi, I have 2 questions: 1. partial fractions: if I have following integral: Itegral[(1-2x^2)/(x - x^3)]dx; my question is do I break down the denominator to x(1-x^2) or do I go further: x(1-x)(1+x); this way it becomes more complicated; 2. chain rule: how does chain rule work in this...

Hi, me with my really old book again. This time , a novel way of turning expressions into partial fractions. It would be best if I show you the examples in the book : \frac{3x^2 +12x +11} {(x+1)(x+2)(x+3)} To express this fraction in the form \frac{A} {x+1} + \frac{B} {x+2} +...

original question: \int (x^2+2x-1)/(x(2x-1)(x+2)) the following is from my math book: 2A + B + 2C = 1 3A + 2B - C = 2 -2A = -1 okay i understand everything the math has done up to this point, this is the point that i don't get: A = 1/2, B = 1/5, C = -1/10 i think the...

Given \frac{2+5x+15x^2}{\left (2-x\right )\left (1+2x^2\right )}=\frac{8}{2-x} + \frac{x-3}{1+2x^2} I am asked to deduce the partial fractions of: \frac{1+5x+30x^2}{\left (1-x\right )\left (1+8x^2\right )} I can solve it using my usual method, but that's not what the question...

I'm making a small mistake somewhere, but I can't seem to find it. \int\frac{dx}{(x-1)(1-2x)} taking the partial fractions 1=A(1-2x)+B(x-1) A=-1, B=-2 \int\frac{-1}{x-1} dx+\int\frac{-2}{1-2x}dx Integrating by substitution, this is what I'm getting -ln(x-1)+ln(1-2x)+C The...

Hi I need some help getting started with this integral \int \frac {x^2+5x+2}{{x^4+x^2+1}}dx Thanks in advance

The integral of [(x+2/(x+4)]^2 A/(x^2+4) + B/[(x^2+4)^2) A=0, B=1 so, the integral of 1/(x^2+4)^2 how do you do this?

here's the problem, i am supposed to take the integral from 1 to 2 of this: (dx)/[(X+3)^2 (x+1)^2] I decided that the easiest way to compute it is by integrating by partial fractions so what i did was set up the equation: A/(x+3) + B/[(x+3)^2] + C/(x+1) + D/[(X+1)^2] = 1 After this I...

hi, i am trying to show that dv/(1- (v^2/v_ter^2)) = g*dt which after integrating is v=v_ter*tanh(g*t/v_ter) (motion with quadratic drag) can also be obtained by using natural logs. so far i have this: letting u = v/v_ter i can use partial fractions to get du/(1-u^2) = 1/2...

i will use "\int" as a integral sign since latex is down. \int (7)/(x^2-1)*dx using partial fractions... took out the 7... 7\int (1)/(x+1)(x-1) A(x-1) + B(x+1) = 7 if x = 1, B=7/2 if x = -1, A= -7/2 ok it's time to set up my integral function: 7\int -7/2(x-1) + 7\int...

Ok this is the Integral: (x^2-1)/((x+2)^2(x+3)) Now What i did is break this up into the A + B+C ...etc etc and i came to this: A/(x+2)^2 + Bx+C/(x+2) + D/X+3... Now i know i got to use systems of equations but I've been working on this for like 40 mins and i still can't get it...

Right, I'm gettin irritated by these :confused: , hehe, I need some expert quidance on how to do all kindsa questions with these, mainly the more complicated 1's where u can't just sub in values of x to get 0. Lotsa input will be appreciated :smile:

hi, the problem is: &int; (8x-17)/x^2+x-12 dx = &int; .../(x+4)(x-3) dx so 8x - 17 = A(x-3) + B(x+4) (A+B)x + 4B - 3A so we have 2 eq and 2 unknown A+B = 8 4B-3A = -17 ... but the book says it's suppose to be 4A - 3B,.. I don't know what I did wrong. Please help.