Fractions Definition and 606 Threads

Like the title says... I should be way past this (in ODEs+Lin. Algebra). I'm just really tired, have a final tomorrow, and cannot for the life of me understand why this works out the way it does. Here goes (and please show most steps, it'd be greatly appreciated, thanks): Start out with...

I'm rather confused on how to operate exponents on fractions. For example (4/3)^-1 or (4/3)^1 Please explain?

Homework Statement find the laurent series of sin(2z)/(z^3) in [z]>0 Homework Equations The Attempt at a Solution I am completely confused. I can understand some of the examples given on laurent series, like using partial fractions and then finding geometric series. Do I rewrite...

Homework Statement evaluate: \int \frac{x^3}{x-1} dx this is part of a bigger question... i get down to this far but i have no idea how to tackle this integral...Homework Equations The Attempt at a Solution my thoughts are - partial fractions... but its only got one thing on the...

Ok I need to know which is the right answer for evaluating the continued fraction \langle 1, 2, 1, 2, \ldots \rangle? Here's my work: x = 1 + \frac{1}{2+x} \Rightarrow x^2 + x - 3 = 0 and by quadratic formula, we get x = \frac{-1 \pm \sqrt{13}}{2} but we only want the positive root so I...

Gamma Function on negative Fractions! If we take a look at the Gamma Function and evaluate the integral by parts then we will get infinity in the first step of Integration by Parts eg: Integral e^-1*x^-5/3 Limits being 0 to Infinity as usual! If we try to integrate this we will get...

Homework Statement A bookstore reduced the price of a book with 25%. After that the sale rose by 10%. Homework Equations With how many percent rose the number of sold books? The Attempt at a Solution i guess it's simply by 10%

Homework Statement ∫ 5e^2x / (25e^2x - 20e^x +4) dx Homework Equations The Attempt at a Solution The attempt at the the solution is in the attachment below. I am stuck at that step. Pretty much can anyone tell me what 'something' should be. I know if the denominator were a...

o/a + h/a =1 how do i flip the h/a fraction? Do i divide them instead of adding them? (Im trying to cancel out the 2 a values)

Homework Statement ∫ dx/(x² -a² ) Homework Equations When (x² -a² ) appears in an integrand, you can use the trig sub: x=asecθ right? The Attempt at a Solution I know I could solve this using partial fractions but why doesn't trip sub work here? Or does it? I have attached my...

Homework Statement Find the volume of the resulting solid if the region under the curve y=1/(x^2+3x+2) from x=0 to x=1 is rotated about the x-axis. R=(1/(x^2+3x+2) Equation for volume using the slicing method... 3.14 INT((1/(x^2+3X+2))^2)dx over the interval 0-1 Homework Equations...

Homework Statement Hello I'm trying to figure out how to integrate with the use of partial fractions but I'm a bit stuck on something that should probably be simple.. but I can't see it clearly How do you split up x2-8/x+3 and make it equal to (x-3) + 1/x+3 or for instance x2 +1/x-1 split up...

Homework Statement \frac{gx^2+1}{x^3(x-1)^2} I'm trying to keep g as a coefficient, it's turning into a mess though. The Attempt at a Solution After I broke it down it gives: Ax^2(x-1)^2 + Bx(x-1)^2 + C(x-1)^2 + Dx^3(x-1) + Ex^3 = gx^2 + 1 After using x =1, everything goes away and I'm...

Help! Infinite continued fractions! Homework Statement -2 + 1 -2 + 1 -2 + 1 -2 + 1 ... an = -2, bn = 1 Homework Equations What is the sum of this indefinite continued fraction, putting this into a quadratic equation? x^2 + 2x - 1 =...

1. find the inverse FT of 1/(iw+3)3 2. well partial fractions gave the same thing back... I'm not sure how to transform this as there's no property that deals with cubics. 3. i tried using the differentiation property but it doesn't work as it increases the power of 3 to 4 and so...

I haven't been able to try all parts of this question yet as I've been running into problems fairly near the start. I've asked for help with it but have just been told 'use the ideal gas law' which is what I tried to do but can't seem to get it right. We have been given answers to parts a, b...

Couldnt we just use whole numbers to graph on the x-axis instead of labeling them pi/2, pi, 3pi/2 ? Because it gets confusing having to memorize which pi fraction goes in order. Is there a better way to memorize these? Thanks

Homework Statement (〖5x^3〗+〖4x^2〗-4)/((x^3)(x+1)) Homework Equations Partial Fractions The Attempt at a Solution I know that I need to use partial fractions. But I don't know how to put it in (A/x)+(B/x)...etc Would someone please kindly show me how to set up this equation...

Homework Statement Solve this IVP: y'=(y-9x)^2 ; y(0)=1 Given a hint: Use the substitution v=y-9x and partial fractions. Homework Equations ... The Attempt at a Solution I was able to solve this DE through partial fractions, etc until I ended up at this point ln (v-3/v+3)...

I am trying to use partial fractions to expand (3200x+16)/(x+400)^2 on the ti-89 calculator but I keep getting .010075 as the answer when I use the expand function! What am I doing wrong here?

Trying to help out a friend. I appolagise if yet again this is in the wrong part of the forum, i haven't an idea what it is categorised as, I am an apprentice engineer and simply that lol Can someone explain how the following is done: x^2 – x + 1 / (x - 2)(x^2 + 1) ≅ A / (x - 2) + Bx +...

Homework Statement Solve the following equations: \frac{1}{x-1} -\frac{1}{x-2} = \frac{1}{x-3} - \frac{1}{x-4} Homework Equations See above. The Attempt at a Solution Rearrangement gives \frac{1}{x-1} -\frac{1}{x-2} - \frac{1}{x-3} + \frac{1}{x-4} = 0 Conversion to...

Homework Statement write out the form of the partial fraction decomposition of the function, do not determine the numerical values of the coefficients x^2/(x^2 + x + 2) Homework Equations The Attempt at a Solution since the numerator is not less of a degree than the...

So I am being asked to use partial fractions to solve ODE's. In particular, I have (dx/dt) = 3x(x-5) with x(0) = 2. I came up with A = -1/5 and B = 15. Then, I had (1/15)*[(x-5)/(3x)] = Be^t. But this is where things break down. I thought B = -1/2. Yet the book's answer is...

Hello to everyone! I need to invert the following infinite continued fraction: 0=\beta_{0}-\frac{\alpha_{0}\gamma_{1}}{\beta_{1}-}\frac{\alpha_{1}\gamma_{2}}{\beta_{2}-}\ldots, n=1..\infty to something starting with the \beta_{n} term and going down to n=1 (where n is the term the fractions...

Homework Statement Integrate: (5x-6)2/x1/2 Homework Equations The Attempt at a Solution I tried substitution, letting u=5x-6 and then plugging that in but realized that I didn't have the proper set up for that. I'm unsure how to go about this; should I factor out the numerator or...

Integration of Rational Functions by Partial Fractions? Ok I'm working on some homework problems and I don't even know how to do the first one, here is my problems and the steps that I did thus far ( I don't know if I did them right) 5x-13/(x-3)(x-2)= A/x-3 + B/x-2\rightarrow ...5x-13=...

Hi Guys, I have a bit of a problem with some course work please help: The question is: Determine the atomic fractions Xc and Xo (carbon and oxygen) for the following gas composition at room temperature: 50% H2, 30% H2O, 20% CO2 I am sure you need to work out the partial pressures for...

Homework Statement Hello, I have a workbook here with a question I am a little confused about, I think it should be quite simple to answer. I know the answer but I don't really understand how it is applied. I know the method but I want clarification on how it works please. The average...

Homework Statement I'm just curious if there is any useful shortcuts when applying partial fractions decomposition. These are only a portion of the problem given for us, so it's important that I can do them quickly and efficiently. Does anyone know of any useful shortcuts that would speed...

Q: Find the Integral of (26x+36)/[(3x-2)(x^2+4)] dx Here is my attempt: First i set it up so that, (26x+36) / [(3x-2)(x^2+4)] = A/(3x-2) + (Bx+C)/(x^2+4) Then, 26x + 36 = A(x^2+4) + (Bx+C)(3x-2) = Ax^2 + 4A + Bx^2+Bx+Cx+C <---(This is where I...

Homework Statement I am stuck on this integral. 1) (a - bx)/(a^2 + b^2 - 2abx)^(3/2) I tried some substitutions but end up with complicated expressions. How to decompose into partial fractions when the denominator is raised to fractional powers? Can anyone please help me out? Homework...

Homework Statement Hi. Bit of a weird question here, was thinking about this and am stumped as to how the following is true. I have a fraction here, http://img109.imageshack.us/img109/2280/math1.jpg I know this equation is definitely true, I have checked it by graphing on my...

1. L-1{(3s+2)/ (s2+2s +10)} After completing the square I get to 3s+2 /(s+1)2 + 32 which suggests two solutions or one. They decompose the fraction into [(A)s+1 /(s+1)2 + 32 ]+ [(B) 3/(s+1)2 + 32] I am unsure of how this decomposition works I thought that we would take A(3s) as the numerator...

Homework Statement \int_0^1 \! \frac{x-4}{x^2+3x+2} dx Homework Equations The Attempt at a Solution Factoring out the denominator... x^2+3x+2 = (x+1)(x+2) Breaking up the main fraction into the separate fractions. Since both are linear, only a single constant is...

Homework Statement \int(5x+2)/(x^{2}+25)^{2}dx Homework Equations The Attempt at a Solution \int5x/(x^{2}+25)^{2}dx+2\int1/(x^{2}+25)^{2}dx I can integrate the first part using u substitution then I am stuck at the second part...my partial fraction answer is the same as the...

Homework Statement Ey guys I am trying to derive a potential flow equation and in the process i need to integrate with respect to 'x'. I need to integrate what is shown below with respect to x Homework Equations -\frac{y^2}{(x^{2} + y^{2})^{2}} The Attempt at a Solution...

I'm having issue with one problem. We're asked to break down the problem into partial fractions to solve for the integral. Well, I'm stuck on one. I'm being asked for the values of A, B, and C for the following problem. ∫((9x^2+13x-83)/((x-3)(x^2 + 16)))dx I can get it worked down...

Hello. These might be easy but I've not done this in years. What are these expressions canceled down? Not homework, I just can't do them. [PLAIN]http://img692.imageshack.us/img692/4849/fractions.png Thanks very much guys.

Hey, I need some help with simplifying these fractions. (3x-6)/(x^2-3x+2) - (x^2-1)/(x^2-4x+4) Im not quite sure what to do with the denominators. Am I supposed to change them to special forms? What is the process of making these a single fraction? Thanks in advance.

Homework Statement Find the real positive number x with periodic continued fraction expansion [0;a,b,a,b,...] where a and b are positive integers. Homework Equations The Attempt at a Solution I have determined that x definitely involves a root.

Homework Statement find the integral of (1 + 2x)/(1+x^2) Homework Equations The Attempt at a Solution I honestly have no idea how to solve this and have spent ages trying to figure it out. I would automatically assume using partial fractions to solve but the denominator presents...

Homework Statement integral of: 1/(((L2)/4)+y2)This is for proving the flux through a cube from a wire going through it is = Qenc/epsilon0 All that's left for one face after taking out constants is the above equation, and I really don't want to go re learn how to do partial fractions again...

16/64 is an unusual fraction such that when you cancel 6's from the top and bottom youre left with correct answer of 1/4. I need to Find a way for finding all other unusal fractions for a fraction n/m such that n>=11 , and m <=99. I have tried writing it as (10a+b)/(10b+c)=a/c ,but stuck...

Hi guys, I know that for integral domains with finte elements that if we show that each element has a multiplicative inverse then it is a field. I need to show that the field of fractions is a field. As the domain is not finite how does that effect the proof of being a field...

Homework Statement dx/dt=3x(x-5); x(0)=2 Homework Equations dx/dt=F(x)G(t) dx/dt=x' The Attempt at a Solution First I separated the variables using F=3x(x-5) and G=3 x'/(3x(x-5))=3 Applying method of quadrature: \int\frac{x'}{(3x(x-5)}dt=\int3 dt On the right hand...

We were discussing them in my math methods class today however I'm not really sure how the idea works. Does anyone know of any online references that might be of some help? Google wasn't much help for me =/

Homework Statement Given: see attachment Five additional electrons are placed at the origin. What is the electric field now. Homework Equations Electric field equations of E=q/(4pi*Eo*r^2) The Attempt at a Solution I am wondering if the electric field would just be 50% higher...

Homework Statement 2 - ((x-3)/(x-2)) ≥ ((x-5)/(x-1)) Homework Equations The Attempt at a Solution I just want to make sure that certain operations that are allowed with fractions in equations are still valid (or not) in inequalities. 2 - ((x-3)/(x-2)) ≥ ((x-5)/(x-1)) Can I...

Homework Statement Evaluate the integral: \int_{1}^2 \frac{4y^2 - 7y -12}{y(y+2)(y-3)}dy Homework Equations None. The Attempt at a Solution \frac{4y^2 -7y -12}{y(y+2)(y-3)} = \frac{A}{y} + \frac{B}{y+2} + \frac{D}{y-3} y = 0: -12 = -6A \rightarrow A=2 y = -2: 16 + 14 -...