Fraction Definition and 653 Threads

Homework Statement a - \frac {a}{1-\frac{a}{1-a}} The Attempt at a Solution \frac{a}{1-a} This might be the part where I am confused. I always get confused when I need to factor out a -1 from this fraction's denominator in order to put it into the form of \frac{a}{a-1} So here...

Can anyone explain why \frac{-1}{x_0^2} (x - x_0) = \frac{-x}{x_0^2} + \frac{1}{x_0}? Is \frac{-1}{x_0^2} (x - x_0) = \frac{-1}{x_0^2} . \frac{(x - x_0)}{1}? After that I multiply to get \frac{-1}{x_0^2} (x - x_0) = \frac{-x + x_0}{x_0^2} = \frac{-x}{x_0^2} + \frac{x_0}{x_0^2}. Then divide...

Homework Statement x^3+1 / x^2+4 Homework Equations The Attempt at a Solution after using long division i get : x + -(4x-1) / (x^2+4) then using partial fraction : -4x-1 / x^2+4 = bx+c / x^2+4 then i am stuck because if what i have is correct then they both are the...

HELP! on Partial Fraction Decomposition Problem! - Heavy Side Technique I am doing a partial fraction decomposition problem for my calc 2 class. We use the Heavy Side Technique, but I will take help either way! \frac{2x-1}{x(x^2+1)^2} Thank you!

Homework Statement \int \frac{x^{2}}{x^{2}-1} Homework Equations The Attempt at a Solution I divide bottom into the top because the degree is the same and get... \int 1-\frac{1}{x^{2}+1} My question is, from here, do I have to recognize the tan^{-1} or is it also correct to...

I'm having some difficulty Solving this partial fraction: (3.84e7)/(s(s^2+6.4e4s+1.6e9))= (3.84e7)/(s(s-3.2e4+j2.4e4)(s-3.2e4-j2.4e4) how do u find the angle? I know the equation but I don't know how to find the B with it conjugate. eq: 2B/_theta but I don't know how to...

Homework Statement 3. Find the partial fraction expansions of the following polynomials a) 10/[(s^2)(s^2+6s+10)] The Attempt at a Solution I assume i should expan the polynomial in the form A/s^2+B/s+(Cs+D)/(s^2+6s+10) but i stuck at finding B. Maybe my expansion is just wrong .. :(

If you have a fraction, for example, \frac{1}{{1.0091532\times10^{-12}} + 1} Is there a simple way to convert it to a more easily calculated form, specifically, 1-x (where x is a very small number)

i am given this function and need to integrate it \frac{4x+7}{\sqrt{-4x^2+20x-9}} i have been trying to intergrate it by calling something T, preferably the expression under the sqrd root, or part thereof (-4x2+20x=T) but i can't find the way to do this, can't find the best expression that...

I'm having trouble finding the derivative of -2x^2+2x-7/x...I'm having trouble understand what to do with the X underneath. Do I bring X to the numerator and make it X^-1 or what? Thanks for your helphttps://www.youtube.com/watch?v=

Homework Statement Homework Equations No clue, honestly I'm trying to figure out what formula i need to use to start this problem. The Attempt at a Solution No clue, honestly I'm trying to figure out what formula i need to use to start this problem.

Homework Statement x3 - x2 - 5x / x2 -3x +2 Homework Equations The Attempt at a Solution Heres what I got 5/x-1 + 6/x-2 but if I multiply those 2 fractions together I do not get a cubic equation on top of the line. I learned how to do these questions with linear equations on...

Hi, Please see the attachment. I really don't understand what the M/7 and the L/13 represents. How did he(authors) logically derive to that? And also, I don't understand how finding the value in-between M/7 and L/13 (M+L/20) helps them come up with the solution and the proof. Thank...

Homework Statement I want to decompose this (s+2)*(s+1)/(s+2)*(s+1)*(s^2+1)-1 using partial fractions so after that i can inverse Laplace it. I have been working on it for several hours but i cannot find a solution. Any help? Homework Equations The Attempt at a Solution

Homework Statement If 100 g H2O contains 11.2 g H, what mass of water could be obtained from 3.06 g H2(g) reacting with an excess of O2(g)? Homework Equations Mass % of X in a sample= (Mass of X in sample/ Mass of the sample)*100 The Attempt at a Solution The parts that confused me...

Problem: A) In a simple cubic arrangement the atoms sit at the corners of imaginary cubes with their curved surfaces just touching. Show that the ratio of filled space to empty space between the atoms is pi/6 or about 0.5. This "packing fraction" is related to the density of the material. The...

Homework Statement When its engine of power 76 kW is generating full power, a small single-engine airplane with mass 660 kg gains altitude at a rate of 2.8 m/s. What fraction of the engine power is being used to make the airplane climb? Homework Equations total power=76x10^3 W mass=660...

[(n+5)/(n-1)]^n i get [infinity/nifinity]^infinity and i don't see anything to change

Homework Statement Find the constant, c, that satisfies the following equation: Homework Equations The integral is from -infinity to infinity 1 = c \int e ^ -|x|/2 *dx The Attempt at a Solution c = 1/4 I have the solution given to me, but I do not understand how to get the...

Homework Statement \frac{4x^{4}-8x^{3}+5x^{2}-2x-1}{2x^{2}-3x-2} Homework Equations The Attempt at a Solution I started of by breaking the bottom part down into (2x+1)(x-2) which then allowed me to set... \frac{A}{(2x+1)}+\frac{B}{(x-2)} The problem is from here I tried...

Fraction is: \frac{1-e^{-x}}{1-e^{x}} and it's meant to go to: -e^{-x} I can't make it look like it needs to. I tried splitting it up but that goes nowhere. What other strategies are there for simplifying fractions like this? Thanks for any help.

im trying to work out how to use partial fractions on a fraction with repeated roots. I am learning about laplace transforms at the moment, i don't remeber the lecturer specifically going through how to solve the transforms that have repeated roots and can't find it anywhere in the lecture...

Homework Statement \int(5sin xcosxdx)/(2+52sinx) The Attempt at a Solution I set u = sinx and du = cosxdx which gives me... \int(5udu)/(2+52u). I just need a little push as where to go from here, not the entire solution, just a push as what to do next. I have a feeling I need to...

this problem should be simple, but i must be doing it wrong. At 250 degrees Celsius, a certain liquid X has a vapor pressure of 900 mm Hg and a second liquid Y has a pressure of 600 mm Hg. What is the minimum mole fraction of X necessary for the mixture to boil at this temperature (assume...

Homework Statement Jane gets in her spaceship on her twenty-fifth birthday and flies to the star Vega at a constant velocity v. She is just turning age 31 when she reaches the Vega system. What is the speed of her ship, as a fraction of the speed of light c? Homework Equations...

Homework Statement \int\frac{2x^{2}}{(x^{2}-1)} dx Homework Equations Partial Fractions The Attempt at a Solution 2\int\frac{x^{2}}{(x^{2}-1)} dx 2\int\frac{x^{2}}{(x-1)(x+1)} dx \frac{A}{x-1} + \frac{B}{x+1} = \frac{x^{2}}{(x+1)(x-1)} A(x+1) + B(x-1) = x^{2} Solving...

Homework Statement In a sample of one litre of carbon dioxide at STP an average of 5 disintegrations C -> N + e + v are observed per minute. Calculate the atomic fraction of C present if the mean lifetime of this nucleus is 8267 years. Homework Equations \tau = \omega-1 = 8267...

Homework Statement sorry I don't know how to type algebraic expressions, but I'll do my best. express quantity [ f(x+h) - f(x) ] over h as a single simplified fraction f is not a variable, it's a function Homework Equations Question # 1. function of x = quantity 1-x over x The Attempt at...

Homework Statement can anyone help me with this problem...i can't seem to figure it out: A 1.222 M solution of a compound in water has a density of 1.3250g/mol at 20 degrees Celsius. what is the mole fraction of this solution? the compound has a molar mass of 97.80g/mol. Homework...

packing fraction of body-centered cubic lattice -- solid state physics Homework Statement This is part of a series of short questions (i.e. prove everything in Kittel Ch. 1, Table 2): Prove that the packing fraction of a BCC (body-centered) cubic lattice is: 1/8 * pi * \sqrt{3}...

Homework Statement what fraction of a centimeter equals 1.0 micrometers Homework Equations prefix for SI units The Attempt at a Solution here's what i did, centi c 10^-2 milli m 10^-3 micro u 10^-6 i started from centi and moved down twice and moved my decimal two more...

Homework Statement I am working on a topic called differential equations, and I am stuck on some working out. 2. Homework Equations [/b] Can someone please help me to factorise the following fraction (u-2)(-u^2+ 3u+ 2) I have to integrate it, and I know I can without factorising, but it...

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) +...

I need help finding the derivative of the following equation. This may look a little messy because it involves a square root and a fraction. y = square root of: 1 + x2 / 3 + 3 - x / 5 My first thought is to change the equation to look like this: y = (1 + x2)1/2 / 3 + 3 - x / 5...

O.k. I am trying to figure out what defines an algebraic fraction. I know it has something to do with the denominator but for the life of me I can not make any sense out of my textbook examples. Like 3/2x = 0 I guess 3/x*x = 3 divided by no actual number which would be zero but that is the...

Homework Statement Determine \int\frac{4x^{2}-2x+2}{4x^{2}-4x+3}dx Homework Equations I believe it's necessary to complete the square. The Attempt at a Solution Completing the square for 4x^{2}-4x+3 gives \int\frac{4x^{2}-2x+2}{(x-\frac{1}{2})^2+\frac{1}{2}}dx let...

Homework Equations \int\sqrt{x^{3}}+1/\sqrt{x}+1 The Attempt at a Solution I tried substitution, but that wouldn't work. I tried integration by parts, but I must not have done it properly since my answer was several factors of x off. Am I missing something?

Problem: Find the integral of 2dx/(2x-3) using partial fraction decomposition Attempt: A/(2x-3) Compare coefficients A = 2 2 \int (1/(2x-3)) = 2ln(2x-3) This is wrong. Can someone please tell me what I'm doing wrong?

Homework Statement Expand the fraction \frac{1}{\sqrt[n]{2^5}}, for n \in \mathbb{N} and n \geq 2, to have denominator 2. Homework EquationsThe Attempt at a Solution \frac{1}{\sqrt[n]{2^5}} \circ \frac{\sqrt[n]{{2}^{n-5}}}{\sqrt[n]{{2}^{n-5}}} \frac{\sqrt[n]{{2}^{n-5}}}{2} Is this correct?

[SOLVED] Alegrabic Fraction Simplification Homework Statement Show that: \frac{3x}{x+1} - \frac{x+7}{x^{2}-1}, x > 1 can be written as: 3 - \frac{4}{x-1} The Attempt at a Solution Well i can see the difference of 2 squares on the bottom of the second fraction...

With the use of Ammonia (R717) properties table, find the enthalpy of the refrigerant if the saturation temperature is -10C and the dryness fraction, x, is 0.9. can anyone help me with this? i do not understand the use of dryness fraction Many thanks!

If anybody can evaluate this, please let me know... Infix notation: 1/(2+3/(4+5/(6+7/(8+9/(10+11/(...)))))) Postfix notation: 1 2 3 4 5 6 ... n ... / + / + / + / + ... / + ...

Homework Statement I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc. [e^(-2s) / (s^2+1)(s-1)(s+1)^2] Homework Equations The Attempt at a Solution I'm not quite sure how to work with the...

An integral with a fraction in it--need help finding the antiderivative Homework Statement I have the integral \int(\frac{20}{1+x^2} - 2)dx where x = ± 3. To solve, I need to find the antiderivative of \frac{20}{1+x^2} - 2 Now, the worksheet actually gives the answer to the problem: The...

Homework Statement Calculate \sum_{n=2}^{\infty}\frac{1}{n^{2}-1} with the "standard" method and with the method of the partial fraction decomposition of the cosine. Homework Equations \pi\cot\pi z=\frac{1}{z}+\sum_{k=1}^{\infty}\frac{2z}{z^{2}-k^{2}} The Attempt at a...

How do I take the derivative of f(x)=ln[x/(x-1)]? Thanks!

Homework Statement (3x-5)/4 + (2-3x)/2 = (x-2)/5 Homework Equations The Attempt at a Solution I tried this and got x= 6.3 reacurring... but i don't think it is right...

Hi guys I have a question? lim x->1 (sqrt(x)-x^2)/(1-sqrt(x)) What is the value of the limit of this function? Is it possible to be (-2)? Or I AM WRONG? Thank you in advance.

Is it possible for me to write this complex fraction as a ratio of two sines? Thanks. \frac{1-e^{101z}}{1-e^{z}}

Homework Statement \lim_{x\to 6}\frac{\sqrt{x+3}-3}{x-6} Homework Equations Answer is 1/6. The Attempt at a Solution \lim_{x\to 6}\frac{\sqrt{x+3}-3}{x-6}=\lim_{x\to 6}\frac{(x+3-9)(x+6)}{(x^2-36)(\sqrt{x+3}+3)}