Fractions Definition and 604 Threads

Homework Statement \frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}} Should equal \left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2} Homework Equations above The Attempt at a Solution...

This is probably a "basic" question, but I can't seem to remember how to do partial fractions problems where there is only a 1 in the numerator. For example (just making this up), let's say I have: 1/s(s+4)(s+5) So what I'd do is 1/s(s+4)(s+5) = A/s + B/(s+4) + C/(s+5) as one would expect...

I'm trying to solve this integral but I'm not sure if I'm on the right track. My question is: can this integral be solved by partial fractions decomposition? I solved the problem that way but I'm not sure if it is the right answer. thanks! ∫1-x+2x^2-x^3 ÷ x(x^2+1)^2

Homework Statement \int\frac{dx}{x(1+ln x)} Homework Equations Partial Fractions? Maybe I am solving this wrong... The Attempt at a Solution \frac{A}{X} + \frac{B}{1+ln x} = 1 A(1+lnx) + Bx =1 A + Alnx + Bx =1 This doesn't seem to work out properly. I have been having a...

is there a way to express any given root of an integer in a continued fraction? i.e. Sqrt[2] = 1 + 1/(2 + Sqrt[2] - 1) and the process can be continued infinitely to get a fraction that defines the radical with only integers. so my question is can this kind of thing be done with any square...

Homework Statement \int {\frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }}ds} The Attempt at a Solution This is a long one...First, I split the integrand into partial fractions and find the coefficients: \begin{gathered} \frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }} = \frac{{As + B}}...

Homework Statement \int {\frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }}ds} The Attempt at a Solution This is a long one...First, I split the integrand into partial fractions and find the coefficients: \begin{gathered} \frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }} = \frac{{As + B}}...

decomposed into TWO "simpler" fractions how would this be decomposed into TWO "simpler" fractions, thanks f(x) = -10x - 7 2x2- 17x +21

Homework Statement Hi everyone, here is a new partial fractions question I just cannot understand: \int\frac{x^{3}}{x^{3}+1}dx Homework Equations Partial Fractions, difference of perfect cubes, polynomial long division The Attempt at a Solution \int\frac{x^{3}}{x^{3}+1} dx...

Homework Statement \[ \int {\frac{{e^t dt}} {{e^{2t} + 3e^t + 2}}} \] I'm not quite sure how to start this one...Any hints? I tried bringing e^t down to the denominator and multiplying it out which still didn't help. I can't see a way to factor the denominator or split this into a...

Homework Statement \int1/(s^{2}(s-1)^{2}) ds Homework Equations Partial Fractions The Attempt at a Solution = \frac{A}{s^{2}}+\frac{B}{s-1}+\frac{C}{(s-1)^{2}} Setting numerators equal to each other: 1 = A(s-1)(s-1)^{2} + Bs^{2}(s-1)^{2}+Cs^{2}(s-1)...

I've been working on this one for a while now but just can't figure it out lim h->0 (1/h) (( 1 / (x + h) ) - ( 1 / x )) my first thought was to figure out (( 1 / (x + h) ) - ( 1 / x )) first by just putting them togeather and then using the congjigate times by one trick but that just...

please... i need a help in integrating the partial fractions i can't proceed to the integration part if i don't understand the patter in finding the constant... that is... if the given is: ʃ ( (x^5+1) / ((x^3)(x+1)) )dx then; ʃ ( x-2 + ( 4x^3+1 ) / ( x^4 + 2x^3) ) ʃ ( x-2 + (...

How do I solve: [sin (pi/3)] + [cos (pi/6)]? <--- "pi" is 3.14... I think that [sin (pi/3)]= (square root 3) divided by 2 AND that [cos (pi/6)]= (square root 3) divided by 2. Now I can't remember how to add fractions containing square roots. My textbook...

Hi, actually, I need to calculate an infinite sum of fractions. The problem is that the Limit of the sum is part of the summands. The formula looks like this: \lim_{n \to \infty} \sum_{i=1}^{n} \frac{1}{n(1 + \lambda + \sigma^2)-i(1+\lambda)}, where 'itex]\sigma[/itex] and \lambda are...

Homework Statement ∫(2t)/(t-3)^2 the integral is 2 to 0 ok does it = A/ t-3 + B/(t-3)^2 I'm not sure if you break up (t-3)^2

Homework Statement ∫1/ x^3-1 dx, ok how would i do this Homework Equations ∫dx/ x^2+a^2= 1/a tan^-1 (x/a) +c i tried to simplify x^3-1 = (x+1)(x-1)(x+1)

Homework Statement ∫ 10/(x-1)(x^2+9) would i change this into 10/ (x-1) (x+3) (x+3) then= A/ x-1 + B/ X+3 + C/ x+3

got an exam coming up in a few days and half way through my question i ran into a partial fractions question instead of having the standard (1/(y+c)(y+d))= A/(y+c) + B(y+d) and multiplying out i had a double root so (1/(y+c)(y+c)) does this change the way i go about the question and are there...

Homework Statement Re-write the following fraction into the sum of fractions: 1/[(n^3)+n] Homework Equations None that I can think of. . . The Attempt at a Solution I first changed [(n^3)+n] to n[(n^2)+1], so by the rules, the aformentioned fraction should equate to (A/n) +...

.. oy, I'm just not sure how to find 3 constants! Here is my problem: 5x^2-4/(x-2)(x+2)(x-1) = A/(x-2)+B/(x+2)+C/(x-1) .. i got a bit of it done, but it's all wrong OH! and what am i supposed to do if the numerator of the first equation does not have any sort of variable with it?? my...

Ok this is something i learned few years ago and I am a bit rusty. So i have to find the absolute value of: \frac{1 - 2i}{3 + 4i} + \frac{i - 4}{6i - 8} So first i add the two fractions and i get: \frac{(1 - 2i)(6i - 8) + (i - 4)(3 + 4i)}{(3 + 4i)(6i - 8)} Next i simplify and then...

how do i find lcm of two fractions ..say.. 2/3 and 5/8 ?? pls help Thank you

For a rational function, (x^2+1)/(x^2-1) = (x^2+1)/[(x+1)(x-1)], if we were to split it into partial fractions so that (x^2+1)/(x^2-1) = A/(x+1) + B/(x-1) = [A(x-1) + B(x+1)]/(x^2-1)...solving for A and B get us A = -1 and B = 1. This would mean that (x^2+1)/(x^2-1) = 2/(x^2-1)...which doesn't...

I'm a little mixed up on the integration for partial fraction decomposition. I basically have x/ x(x^2 + 1) I'm wondering for the (x^2 + 1) part, am I to put Ax + B over it because it is a raised power, or since the outside bracket is not squared, it is to only have one variable over it.

Homework Statement we have 4/((s^2) + 4)(s-1)(s+3) Homework Equations The Attempt at a Solution dividing it up do we get: A/((s^2) + 4) + B/(s-1) + C/(s+3) = 4 or is it (As + B)/((s^2) + 4) + C/(s-1) + D/(s+3) = 4

Homework Statement [e^(-2s)] / (s^2+s-2) Find the inverse Laplace transform. Homework Equations The Attempt at a Solution I know that I can factor the denominator into (s+2)(s-1). Then I tried to use partial fractions to split up the denominator, but I don't know how to do that...

Is there any way to derive the greatest common divisor from the prime factorizations of the numerator and denominator? For instance: \displaystyle{\frac{48}{150} = \frac{ 2 * 2 * 2 * 2 * 3}{2 * 3 * 5 * 5}} The GCD = 6 in this example, but is there any way to determine that from the...

Homework Statement Suppose a_n > 0, s_n =a_1 + ... + a_n, and \sum a_n diverges, a) Prove that \sum \frac{a_n}{1+a_n} diverges. Homework Equations The Attempt at a Solution Comparison with a_n fails miserably.

Homework Statement 1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c) Homework Equations Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. The Attempt at a Solution As I said, without somehow simplifying it at the start...

Telescoping Method & Partial Fractions...PLEASE HELP! Homework Statement Find the sum of the series from n=1 to infinity... 2/(4n^2-1) Homework Equations The Attempt at a Solution I want to use the telescoping method... 2/(4n^2) = 2/[(2n-2) * (2n+1)] I am following an...

Hello all, I've got an exam tomorrow so any quick responses would be appreciated. I'm following the Boas section on Laurent series... Anyway, here's my problem: In an example Boas starts with f(z) = 12/(z(2-z)(1+z), and then using partial fractions arrives at f(z) = (4/z)(1/(1+z) +...

(t+1) dx/dt = x^2 + 1 (t > -1), x(0) = pi/4 I have attempted to work this by placing like terms on either side and then integrating. 1/(x^2 + 1) dx = 1/(t + 1) dt arctan x = ln |t + 1| + C x = tan (ln |t + 1|) + C pi/4 = tan(ln |0 + 1|) + C pi/4 = C x = tan (ln |t + 1|)...

in HEP, what exactly is the definition of soft particle? also, why are branching fractions \Gamma in GeV instead of a unitless ratio?

Homework Statement Solve y"+4y'=sin 3t subject to y(0)=y'(0)=0 using Laplace Transform The Attempt at a Solution So I got: s^2Y(s)-sy(0)-y'(0)+4[sY(s)-y(0)]=\frac{3}{s^2+9} \Rightarrow Y(s)=\frac{3}{(s^2+9)(s^2+4)} Now it looks like two irreducible quadratics, which I...

Starting with simple fractions, it's known that: {{{a \over b}} \over {{c \over d}}} = {{ad} \over {bc}} So when b == d: {{{a \over b}} \over {{c \over b}}} = {a \over c} But what if in the case of: {{{{1 + \sqrt 2 } \over {\sqrt 2 }}} \over {{{1 - \sqrt 2 } \over {\sqrt 2 }}}}...

http://img340.imageshack.us/img340/1967/25616732jw6.jpg i got answer of 0.4 by trial and error, but i have seem to forgotten the basic of fraction... please guide me thanks

[SOLVED] Partial Fractions 1. Evaluate: \int \frac{dx}{x^{2} -1} Attempt: \int \frac{dx}{x^{2} -1} = \int \frac{dx}{(x+1)(x-1)} = \frac{A}{(x+1)} + \frac{B}{(x-1)} = \frac{Ax - A + Bx + B}{(x+1)(x-1)} Where do I got from here? Thanks

How do you get 3/sqrt2 from 3sqrt2/2?

Homework Statement Evaluate the indefinite integral. int (6 x + 7)/(x^2 + 1) dx ` The Attempt at a Solution A/(x + 1) + B/(x - 1) 6x + 7 = A(x - 1) + B(x + 1) 6x + 7 = (A + B)x + (-A + B) A + B = 6 -A + B = 7 A + (7 + A) = 6 2A = -1. A = -.5 B = 3.5 So the...

Homework Statement Turn this into partial fraction. k1b1/[((k1+b1*s)(k2+b2*s))-b1^{2}s^{2}] Homework Equations n/a The Attempt at a Solution original question was to find the transfer function with springs and a damper and I reduced it to this far but I can't get the partial...

This is a calculus equation, but I'm having trouble with the algebra part of it. http://calcchat.tdlc.com/solutionart/calc8e/02/e/se02e01045.gif I'm confused about how they simplify from step 4 to 5. Can someone help me?

[SOLVED] integration by partial fractions Homework Statement \int((2x^2-1)/(4x-1)(x^2+1))dx Homework Equations A[SIZE="1"]1/ax+b + A[SIZE="1"]2/(ax+b)^2 + ... + A[SIZE="1"]n/(ax+b)^n The Attempt at a Solution (2x^2-1)/(4x-1)(x^2+1) = A/4x-1 + Bx+C/x^2+1 2x^2-1/x^2+1 = A +...

Homework Statement I don't understand why cross multiplying (a+1) with a(a+1) = (a+1)^2. Similary on the RHS, I don't understand why cross multiplying (a-1) with a(a-1) = (a-1)^2. Homework Equations Factorizing to next step: \frac{a + 1}{a(a - 1)} _ \frac{a-1}{a(a + 1)}...

Integrate using partial fractions: (int) (x^3)/(x^2 -1) dx I have put into the form (int) (x^3)/((x-1)(x+1)) dx I thought partial fractions had this property: 'Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator.'...

--Here is an article taken from the USAToday that talks about the teaching and learning of mathematic fractions and some controversal opinions arises with this matter. Feel free to discuss what you think of this. I'm personally curious of the different points of views on this issue...

I am taking college algebra this semester at my Community College. Prerequisite for pre-calculus . I have been doing good in math, but i have done fractions on calculator. I really don't know how to solve fractions (Addition & Subtractions) Problems without calculator.Please explain me how to...

Homework Statement Integration of 1/(x^2-5x+6) Homework Equations The Attempt at a Solution I know i cannot do ln|x^2-5x+6| I've tried some form of substitution or intergration by parts, and they don't work. Should I factor the bottom?

Homework Statement The problem is from Stewart, Appendix G, A58, no.45. Suppose that F, G, and Q are polynomials, and: F(x)/Q(x) = G(x)/Q(x) for all x except when Q(x) = 0. Prove that F(x) = G(x) for all x. [Hint: Use Continuity] The Attempt at a Solution I thought the statement was...

I have a question regarding various planes in an FCC, and determine their packing fractions. I searched but couldn't find anything :) For example, one of the planes is the (100) plane, and I have said there are 2 full atoms (1 in the middle, and 4 quarters from each side), distance 'a'...