Fractions Definition and 607 Threads

Problem with factorising Hi, the question is to differentiate the following equation with respect to x. x^4(3x-1)^3 Using the product rule i think i'v partially completed this to x^4(3(3x-1)^2) + (3x-1)^3(4x^3) I'm now required to simplify this - which leaves me completely stumped...

I'm wondering about fractions, and how I can simplify them. If they're small like 6/10, I see it straight away, but if they're big like 122/163, I don't really know where to start without resorting to random trial and error... Isn't there a more structural procedure to simplify fractions as...

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

I am stuck how to determine a general formula for tn+1 in terms of tn given that the 'infinite fraction' as a sequence of terms tn is : t1 = 1+1 t2 = 1 + __1__ 1+1 t3 = 1 + ___1___ 1 + __1__ 1+1 It involves the fibonacci sequence.

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 need some help Simplifying Complex Fractions. Here are some of the questions: http://learn.flvs.net/webdav/educator_algebra2_v5/Module6/ImagMod6/M6_07_10.gif http://learn.flvs.net/webdav/educator_algebra2_v5/Module6/ImagMod6/M6_07_11.gif...

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...

When I write out the decimal expansion of 1/p where p is a prime, it is always a recurring decimal with a period per(p). I was thinking why inverting a prime number should always give a recurring decimal but could not think of a reason other than it has to be something to do with our base 10...

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:

Finding the antiderivative for fractions? Hello, I get antiderivatives and the idea behind them. But I still don't really comprehend how to apply it towards a fraction. We know that \int (\frac{1}{x}) dx = ln|x| So would the antiderivative of \int (\frac{4}{x}) dx = 4(ln x) ? But...

Hi there all smart people! I'm doing some work on continued fractions of this type: http://viitanen.se/cf.gif I'w worked out an formula for the exact value of tn and I'm now looking for limitations for that formula... K≠-1 is one limitation since it will give dev. by 0. My question now is...

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 so I have to find the arc length from t=1 to t=2. \begin{array}{l} L = \int_a^b {|r'(t)|dt} \\ |r'(t)| = \frac{{2(1 + 2t^4 )}}{{t^3 }} \\ \end{array} And I have completely forgotten how to integrate fractions... Oh wait... i THINK i know what to do. Should i set u=1+2t^4?

Hey having a bit of trouble with this question, not sure what to do! QUESTION - express the fraction in the form a + b rootc / d 3 + root24 / 2 + root6 ------------------------------------------ (3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6) Simplifying gives (6 -...

Apparently I've forgotten how to simplify algebraic fractions. I included the problem as a picture. http://community.webshots.com/photo/461491683/476214616XrKOZJ#" I can't figure out how they went from the red box and then to the green box and then the blue box. Obviously, I understand from...

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...

I'm about to do a test in a couple of days on a course titled "Topics in Pure and Experimental Maths". I was looking over some of the examples we have been given and I have utterly forgotten how to solve Diophantine Equations using Continued Fractions, could some one point me on the right track...

We just started this and I mostly understand it except when it comes to using A, B, C, etc substitution. What I mean is this, here is an exampe. (6x^2+x+1)/(x^2+1)(x-1) = (Ax+B)/(x^2+1) + (C)/(x-1) You then multiply by denominators so you end up with (Ax+B)*(x-1) + (C)*(x^2+1). You...

Since I can't write if a number is squared or anything I'll show you what I'm going to do. If X is squared I will just write x(x) That is what will represent squared. And since these are fractions I will use a slash to distinguish between the numerator and denominator. x(x) / (x-1)(x-1) MINUS...

Fractions of distillation... Some of the fractions which result from fractional distillation seem to share carbons of the same length - yet these form different fractions. Why? Eg - Petrol is carbon chain length 4 - 12, naptha is 7 - 14 and kerosine is 11 -15; why the overlap when they boil...

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} +...

no idea how to simplify this one: sqrt [1- [(x-1)^2/(x+1)^2]] thanks dave

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...

Simplify (x+1)/(x-1) multiplied by (x+3)/(1-x^2) divided by (x+3)^2/(1-x) Im not sure how to factor the 1-x^2 and what to do with 1-x I don't know how to simplify this please help someone. The answer to this question is 1/(x-1)(x+3) x cannot = 1,-1, and -3

Hi. I am starting the study of series and I don't see how to do this problem. "Show that \sum_{n=0}^\infty \frac{1}{(n+a)(n+1+a)} = \frac{1}{a}" All i got is the decomposition in partial fractions as \sum_{n=0}^\infty (...) = \sum_{n=0}^\infty \frac{1}{(n+a)} + \sum_{n=0}^\infty...

find real and complex part of z: z/z+2=2-i I can't factor out the z because of the 2 in the denominator. The i can be written as the square root of -1 but that doesn't help. I tried multiplying by the conjugate to get z alone but nope not any good. I am doing something wrong can someone...

I am having difficulty putting this question...i can't explain exactly what i mean Can anyone tell me in detail (history, number theory and all) about multiplication of fractions? I know that 5^2 means taking 5, 5 times and adding them. But what does 0.5^70 mean? I need indepth...

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

Hi all, I've been fighting with this limit: \lim_{n \rightarrow \infty} \left( \frac{1}{2} + \frac{3}{2^2} + \frac{5}{2^3} + \frac{7}{2^4} + ... + \frac{2n - 1}{2^n} \right) What I did so far: \lim_{n \rightarrow \infty} \left( \frac{1}{2} + \frac{3}{2^2} + \frac{5}{2^3} +...

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...

chromatography: we have to collect the fractions from the column. i wonder what is the difference between; flowthrough fraction, wash fraction and eluate fraction? i think i know what it means with eluate fraction, but what about the other two? hope for replies! thanks a bunch!

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...

Hi can anyone tell me what is tan 50 in fractions? -benzun

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...